What object should one focus on when meditating to reduce anxiousness?

I think it depends on the person's personality. Mindfulness of fear is pretty effective. Just like the Buddha saying to Mara, "I see you, Mara". I recently read an article called Inviting Mara To Tea. It talked about welcoming and thanking Mara. Treating Mara as a messenger to teach you.

In line with that, I think the Brahmavihara should be quite effective. It diverts your mind from your own fear, and redirects it to the welfare of others. It changes your mind from negative to positive.
Metta (loving kindness)
Karuna (compassion)
Mudita (empathic joy for others)
Upekkha (equanimity, even-mindedness to everyone)

Saripathana based on breath and walking meditation could be the best. I am more inclined to practice walking meditation.

https://www.youtube.com/watch?v=ngEhlYiM--E&t=2s

Try to remove notions of "I", "mine", "myself" and fear/anxiety will have no anchor to latch onto:

"Herein, Bahiya, you should train yourself thus: 'In the seen will be merely what is seen; in the heard will be merely what is heard; in the sensed will be merely what is sensed; in the cognized will be merely what is cognized.' In this way you should train yourself, Bahiya.

"When, Bahiya, for you in the seen is merely what is seen... in the cognized is merely what is cognized, then, Bahiya, you will not be 'with that.' When, Bahiya, you are not 'with that,' then, Bahiya, you will not be 'in that.' When, Bahiya, you are not 'in that,' then, Bahiya, you will be neither here nor beyond nor in between the two. Just this is the end of suffering." ~~ Ud 1.10 ~~

There is unrest of mind; frequently giving unwise attention to it — that is the nourishment for the arising of restlessness and remorse that have not yet arisen, and for the increase and strengthening of restlessness and remorse that have already arisen. — SN 46:51

Denourishing of Restlessness and Remorse

There is quietude of mind; frequently giving wise attention to it — that is the denourishing of the arising of restlessness and remorse that have not yet arisen, and of the increase and strengthening of restlessness and remorse that have already arisen. — SN 46:51

"Monks, when the mind is agitated, that is the wrong time to cultivate the enlightenment-factors of investigation-of-states, of energy, of rapture. Why? An agitated mind is hard to calm through these factors. "When the mind is agitated, that is the right time to cultivate the enlightenment-factors of tranquillity [1. passadhi], concentration [2. samadhi], equanimity [3. upekkha]. Why? Because an agitated mind is easy to calm through these factors. [...] As for mindfulness [4. Sati] that is always useful. -Aggi Sutta

Here the meaning of the principles;

1. Passadhi

   Therein what is calmness-awakening-factor? That which of the aggregate of feeling, of the aggregate of perception, of the aggregate of volitional activities, of the aggregate of consciousness is calmness, serenity, being calm, being serene, state of being serene, calmness-awakening-factor. This is called calmness-awakening-factor. (5)For him of raptureful mind the body (of mental aggregates) becomes calm, also consciousness becomes calm. This is called calmness-awakening-factor.

The serenity, the composure which there is on that occasion, the calming, the tranquillizing, the tranquillity of the aggregates

2. Samadhi

   Unshakability by agitation as the meaning of the concentration power

Therein what is samādhi-awakening-factor? That which is stability of consciousness. right samādhi, samādhi-awakening-factor, path constituent, included in the path. This is called samādhi-awakening-factor. For him of calm body (of mental aggregates) and mental pleasure, consciousness is in samādhi. This is called samādhi-awakening-factor.

The stability, solidity, absorbed steadfastness of thought which on that occasion is the absence of distraction, balance, imperturbed mental procedure, quiet, the faculty and the power of concentration, right concentration—this is same as composure [collectedness/self-collectedness/onepointedness]

3. Upekkha

   Therein what is equanimity-awakening-factor? That which is equanimity, having equanimity, supreme equanimity, state of balance of consciousness, equanimity-awakening-factor. This is called equanimity-awakening-factor. He, having consciousness in samādhi in the above manner, is well balanced. This is called equanimity-awakening-factor.

The mental [condition] neither pleasant nor unpleasant, which, on that occasion, is born of contact with the appropriate element of representative intellection; the sensation, born of contact with thought, which is neither easeful nor painful; the feeling, born of contact with thought, which is neither easeful nor painful—this is the feeling that there then is.

4. Sati

   Unshakability by negligence as the meaning of the mindfulness power

Therein what is mindfulness-awakening-factor? Herein a monk is mindful, furnished with excellent mindfulness-penetration, he remembers, remembers constantly, what has long been done and long been said (concerning release). This is called mindfulness-awakening-factor.

That which is mindfulness, recollection, recall, mindfulness, remembrance, bearing (in mind), not losing, not confusing, mindfulness, the Faculty of Mindfulness, the Strength of Mindfulness, Right Mindfulness: this is called ‘mindfulness.’

The mindfulness which on that occasion is recollecting, calling back to mind; the mindfulness which is remembering, bearing in mind, the opposite of superficiality and of obliviousness; mindfulness as faculty, mindfulness as power, right mindfulness—this is the faculty of mindfulness that there then is. - vibhanga

The Blessed One said, “Suppose, monks, that a large crowd of people comes thronging together, saying, ‘The beauty queen! The beauty queen!’ And suppose that the beauty queen is highly accomplished at singing & dancing, so that an even greater crowd comes thronging, saying, ‘The beauty queen is singing! The beauty queen is dancing!’ Then a man comes along, desiring life & shrinking from death, desiring pleasure & abhorring pain. They say to him, ‘Now look here, mister. You must take this bowl filled to the brim with oil and carry it on your head in between the great crowd & the beauty queen. A man with a raised sword will follow right behind you, and wherever you spill even a drop of oil, right there will he cut off your head.’ Now what do you think, monks: Will that man, not paying attention to the bowl of oil, let himself get distracted outside?” “No, lord.” “I have given you this parable to convey a meaning. The meaning is this: The bowl filled to the brim with oil stands for mindfulness immersed in the body. Thus you should train yourselves: ‘We will develop mindfulness immersed in the body. We will pursue it, hand it the reins and take it as a basis, give it a grounding, steady it, consolidate it, and undertake it well.’ That is how you should train yourselves.”

Some notes on these;

When developing the passadhi, mindfulness of the in&out breathing which is then mindfulness of bodily fabrications as in things tied to the body, that is usually the go-to for object of meditation.

When developing the samadhi, it's power is that of unshakability by agitation. Non-distraction is to be known as the meaning of the concentration faculty.

When developing uppekha, i primarily use the theme of four primary elements that are internal or external. I also think that one may use the theme of general unattractiveness which ie is in case of the body generally tied to the graveyard contemplations given in the Satipatthana Sutta but isn't limited to it, if one practices those equanimity or loathing will be established. Id also use 'non-delight in all worlds' and like Vsm suggest general contemplation of dhamma tied to unattractiveness, impermanence, drawbacks and whatever else makes one reject the bait.

The commentary of Vsm lists six things as conducive to the abandonment of restlessness and remorse:

1. Knowledge and pondering of the Dhamma;
2. Asking questions about the Dhamma;
3. Familiarity with the Vinaya (the Code of Monastic Discipline, and for lay followers, with the principles of moral conduct);
4. Association with those mature in age and experience, who possess dignity, restraint and calm;
5. Noble friendship;
6. Suitable conversation.

In general i think one should investigate the cause of anxiety to address it most appropriately and if one can't know the cause one probably has to cover all the bases because anxiety manifests due to many things like one's behavior, views, fears, regrets and resolves.

Where no references it's either patisambhidamagga or vibhanga, except that sutta excerpt w beauty queen that is sutta pitaka.

Just feel the body in general as one breath in and out. Then allow the body to relax. As the body relaxes, so does the cognitive mind.