Does Shikantaza lead towards attaining Jhana, if not, is there any progression?

It's good, that you know your comfort zone. But if you do not come out of it and instead get trapped yourself there, then it's not good.

The purpose of meditation is to get rid of meditation. In fact, the purpose of any practice is to get rid of practice. It's like train, you get in from your home and get down when you reach.

So I suggest you do breath meditation because it brings disturbance and then periodically or whenever you realise you are trapped in thoughts then gently move to your comfort zone.

Later you should aim to be in meditative state throughout the day, while working, sleeping, eating, and amid all walks of life.

If you never come out of your comfort zone, your sankhara will always wait outside your comfort zone and in the battle zone.

If Shikantaza helps you stop thoughts, then it's useful for that. That's a necessary skill for entering second jhana. If breath meditation is triggering thoughts, you're not doing it correctly. The main point of that meditation is to give your mind a physical, interesting, pleasant object to occupy your attention so there's no room and no time for stray thoughts.

Another big problem is Goenka system, as well as Late Theravada teaches a very different breath meditation than what the early buddhist suttas teach. If you follow the early suttas, such as here on breath meditation, https://lucid24.org/sted/16aps/index.html (contains many resources compliant to early buddhist suttas on the topic, including my translation and interpretation of the sutta on breath meditation), then having the sensitivity and full body awareness is much easier to lock in on pleasant sensations of breath and stay focused. Whereas late buddhist technique of being "one pointed at the nostril to the exclusion of the rest of the body" tends to cause many problems like hypertension, head aches, boredom, frustration, tense and uncomfortable body from tight focus, etc.

Without a teacher and teaching, meditation alone may succeed. Indeed, the Buddha own insight and practice were ultimately required for his enlightenment. The Buddha had teachers that brought him to a certain point, but he had to go further on his own.

DN34:1.6.95: Furthermore, it may be that neither the Teacher nor … the mendicant teaches Dhamma … nor does the mendicant recite the teaching … or think about it.
DN34:1.6.96: But a meditation subject as a foundation of immersion is properly grasped, attended, borne in mind, and comprehended with wisdom.

However, for the rest of us, the words of another are quite important--they help save make the best use of time in this very life.

AN2.126:1.1: “There are two conditions for the arising of right view.
AN2.126:1.2: What two?
AN2.126:1.3: The words of another and proper attention.

Regarding meditative bliss, the Buddha acknowledges the attraction. The Buddha also gently reminds us that we should extend our practice to include others:

MN8:4.1: It’s possible that a certain mendicant, quite secluded from sensual pleasures, secluded from unskillful qualities, might enter and remain in the first absorption, which has the rapture and bliss born of seclusion, while placing the mind and keeping it connected.
MN8:4.2: They might think
MN8:4.3: they’re practicing self-effacement.
MN8:4.4: But in the training of the Noble One these are not called ‘self-effacement’;
MN8:4.5: they’re called ‘blissful meditations in the present life’.

I practiced formal zazen for over a decade under the guidance of Tanouye Tenshin Roshi and his students. Zazen has been tremendously helpful to my life. So are the words of the Buddha and good spiritual friends.

p.s., regarding breaths and getting lost, for decades I have simply counted my breath. Keeping the count is easier than trying to fight distracting thoughts.

Ven. Ajahn Brahm is widely recognized as an expert of samatha meditation leading to jhana from mindfulness of breathing, with his book, "Mindfulness, Bliss and Beyond".

I quote a part of this book below.

Here, he explains the transition from focusing and watching the breath, to the entry point into jhana.

There's a point where the mind simply lets go of everything and simply stays with the peace and bliss of the breath, and finally drops the focus on the breath, and stays with the peace and bliss, which is at the "center of the experience of breath", like the stillness at the center of the eye of a cyclone.

To get there, ironically, the mind has to let go, and not grasp anything. It must simply be, and not try to become.

In other words, you start with mindfulness of breathing, and then reach the stage of "just sitting" (sounds familiar?) and then from there, could progress into jhana (a deeper "just sitting").

And the terms jhana, dhyana, ch'an and zen all mean the same thing in different languages.

So, Shikantaza ("just sitting") is not really a totally different and unrelated meditation, in my opinion, based on what I have heard of it.

You experience every part of each in-breath and out-breath continuously for many hundred breaths in a row. That is why this stage is called full sustained attention on the breath. You cannot reach this stage through force, through holding or gripping. You can attain this degree of stillness only by letting go of everything in the entire universe except for this momentary experience of the breath happening silently. Actually “you” do not reach this stage, the mind does. The mind does the work itself. The mind recognizes this stage to be a very peaceful and pleasant place to abide, just being alone with the breath. This is where the doer, the major part of one’s ego, starts to disappear.

One finds that progress happens effortlessly at this stage of meditation. We just have to get out of the way, let go, and watch it all happen. The mind will automatically incline, if we only let it, toward this very simple, peaceful, and delicious unity of being alone with one thing, just being with the breath in each and every moment. This is the unity of mind, the unity in the moment, the unity in stillness.

The fourth stage is what I call the “springboard” of meditation, because from it one may dive into the blissful states. When we simply maintain this unity of consciousness by not interfering, the breath will begin to disappear. The breath appears to fade away as the mind focuses instead on what is at the center of the experience of breath, which is awesome peace, freedom, and bliss.

At this stage I introduce the term “beautiful breath.” Here the mind recognizes that this peaceful breath is extraordinarily beautiful. We are aware of this beautiful breath continuously, moment after moment, with no break in the chain of experience. We are aware only of the beautiful breath, without effort and for a very long time.

Now as I will explain further in the next chapter, when the breath disappears, all that is left is “the beautiful.” Disembodied beauty becomes the sole object of the mind. The mind is now taking the mind as its own object. We are no longer aware of the breath, body, thought, sound, or outside world. All that we are aware of is beauty, peace, bliss, light, or whatever our perception will later call it. We are experiencing only beauty, continuously, effortlessly, with nothing being beautiful! We have long ago let go of chatter, let go of descriptions and assessments. Here the mind is so still that it cannot say anything. One is just beginning to experience the first flowering of bliss in the mind. That bliss will develop, grow, and become very firm and strong. And then one may enter into those states of meditation called the jhanas.

Stop craving attainment and obsessing about attainments. Shikantaza is just sitting, no jhanas, no BS. You know you have this thorn stuck deep inside your heart, you want to be special, your want to be an achiever. That's the poison that's eating you alive, your worldly life and your Buddhist practice. You gotta let go.

Of course you can. Think of the etymology - zen -> chan -> dhyana -> jhana. It's the same word bastardized and modified over the course of four languages. Zen is absorption practice. It's what the Buddha taught although to be fair the methodologies are slightly different.

But get off the idea of jhana. It's not important. Whether you are in the second, the fourth, the realm of infinite space, etc. the phenomenology of these states is irrelevant. What is important is what these states prepare the mind for - namely insight. As practitioners of Zen, we go into emptiness to purify our body, mind, and heart. We then take that supple openess and bring it back to the world of form and investigates our own personal hang-ups, obstacles, and general bullshit. This can be done in a number of different ways - regular vipassana practice of really any stripe, koans, or simply washing our bowl. It's the intersection of form and emptiness that is the catalyst for liberation. The means for setting up that intersection are limitless, but it all starts with quieting the mind through zazen.

Zen doesn't "teach" the jhanas because so as long as insight is happening, the nature of the state we're able to reach isn't important. We just sit and open up. If the first jhana arises, great. If we are antsy, great. It doesn't matter. Just keep sitting and see what happens. Train to be, not to become.