What is Buddhism (in a nutshell)?

"The second reason for regarding the scholastic approach as misguided can be seen in all the evidence we have cited that the Buddha was not trying to build a systematic description of reality — or ultimate realities — as a whole. Thus to try to create one out of the raw materials of his words is a misapplication of his teaching — a form of inappropriate attention that distracts from the actual practice of his teachings, and one he would not condone.

Here it’s useful to remember the Buddha’s own analogy for his project as a teacher. From the first day of his teaching to the last, he stated that he was teaching a path. He started not with a first principle, but with a self-evident problem — stress — and then showed a path to its solution. Instead of trying to provide a total account of the world, he was simply showing the route to a particular goal where the initial problem is solved."

~ Thanissaro Bhikkhu "Skill in Questions: How the Buddha Taught" https://www.dhammatalks.org/books/SkillInQuestions/Section0008.html

In a nutshell:

• The Buddha taught that there is suffering, the cause of suffering, the cessation of suffering and the way to end suffering permanently.
• Suffering is in the mind and originated by the mind.
• To permanently end suffering, one must let go of mentally clinging to impermanent and unreliable things that are not you and do not belong to you.
• The Noble Eightfold Path is the systematic way that leads to the permanent end of suffering.

Formerly and also now, I make known just suffering and the cessation of suffering.
SN 22.86

The noble truths of suffering, the origin of suffering, the cessation of suffering, and the practice that leads to the cessation of suffering.
MN 141

Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts, suffering follows him like the wheel that follows the foot of the ox.

Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts, happiness follows him like his never-departing shadow.
Dhammapada 1-2

“Bhikkhus, suppose there was a mountain river sweeping downwards, flowing into the distance with a swift current. If on either bank of the river kasa grass or kusa grass were to grow, it would overhang it; if rushes, reeds, or trees were to grow, they would overhang it. If a man being carried along by the current should grasp the kasa grass, it would break off and he would thereby meet with calamity and disaster; if he should grasp the kusa grass, it would break off and he would thereby meet with calamity and disaster; if he should grasp the rushes, reeds, or trees, they would break off and he would thereby meet with calamity and disaster.

“So too, bhikkhus, the uninstructed worldling … regards form as self, or self as possessing form, or form as in self, or self as in form. That form of his disintegrates and he thereby meets with calamity and disaster. He regards feeling as self … perception as self … volitional formations as self … consciousness as self, or self as possessing consciousness, or consciousness as in self, or self as in consciousness. That consciousness of his disintegrates and he thereby meets with calamity and disaster.
SN 22.93

“Bhikkhus, what do you think? If people carried off the grass, sticks, branches, and leaves in this Jeta Grove, or burned them, or did what they liked with them, would you think: ‘People are carrying us off or burning us or doing what they like with us’?”—“No, venerable sir. Why not? Because that is neither our self nor what belongs to our self.”—“So too, bhikkhus, whatever is not yours, abandon it; when you have abandoned it, that will lead to your welfare and happiness for a long time. What is it that is not yours? Material form is not yours… Feeling is not yours… Perception is not yours… Formations are not yours… Consciousness is not yours. Abandon it. When you have abandoned it, that will lead to your welfare and happiness for a long time.
MN 22

For a wise person who has arrived at true knowledge, right view springs up. For one of right view, right intention springs up. For one of right intention, right speech springs up. For one of right speech, right action springs up. For one of right action, right livelihood springs up. For one of right livelihood, right effort springs up. For one of right effort, right mindfulness springs up. For one of right mindfulness, right concentration springs up.
SN 45.1

The distinguishing factor of a religion is soteriology — theory of salvation — which has two components:

• An assertion (or recognition, perhaps) that life in the temporal world contains trials, tribulations, miseries, pains, etc.: an array of unpleasant and (mostly) unavoidable happenings.
• An assertion that it is possible to reach a place where those unpleasant happenings do not exist, through some particular programme of action.

Religious philosophy, thus, differs from political, moral, or social philosophy because the latter try to make the temporal world a better place, while religious philosophy tries to transcend the temporal world to reach an idealized state.

There are a number of different soteriologies out there in the world, But Buddhism's boils down to the following:

• The source of human misery is rooted in ignorance — misunderstandings of the true nature of reality — and attachments to the mental fabrications that arise from such ignorance. Our misunderstandings and attachments cause us to constantly recreate the conditions of misery that we are trying to escape. It's a bit like that old saying about how drunks or crazy people keep doing the same thing while expecting to get different results...
• Through a careful programme of developing awareness (through study, contemplation, and meditation), one will come to understand the true nature of reality, eliminating misunderstandings and obviating any attachments to those misunderstandings. Then one will abide in a state of peace and joy.

I don't see that as 'letsist', particularly, and the term 'spiritual' is too vaguely defined to make many fine distinctions of this sort. Take it as you will...