Most frequent realms for post-human rebirth

The condition for birth is bhava and the condition for bhava is craving for sensual pleasure, for existence and for non-existence. Puthujjanas and animals have all 3. Plus it would be weird that animals do not have sensual pleasure but humans do. And since nobody has ''only craving for sensual pleasure'', the other 3 cravings must be there as well for animals. The only people who do not have craving for sensual pleasure are some enlightened devas and the human anagamins and Arhats. Unenlightened devas have the 3 cravings.

For the humans and their traits (physical or not ) from past karma, the most famous sutta is https://www.accesstoinsight.org/tipitaka/mn/mn.135.than.html

In the Pali suttas, non-Dhamma speech is called "animal talk" ("tiracchāna kathaṃ") as follows:

At one time the Buddha was staying near Sāvatthī in Jeta’s Grove, Anāthapiṇḍika’s monastery. Now at that time, after the meal, on return from alms-round, several mendicants sat together in the meeting hall. They engaged in all kinds of unworthy [animal] talk (tiracchānakathaṃ), such as talk about kings, bandits, and ministers; talk about armies, threats, and wars; talk about food, drink, clothes, and beds; talk about garlands and fragrances; talk about family, vehicles, villages, towns, cities, and countries; talk about women and heroes; street talk and well talk; talk about the departed; motley talk; tales of land and sea; and talk about being reborn in this or that state of existence.

https://suttacentral.net/an10.69/en/sujato

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tiracchāna: going crosswise or obliquely or horizontally; an animal; a (non-human)

kathā: talking, talk, conversation; discussion; a talk, discourse; an account, a story.

The above shows the word "tiracchāna" does not refer to literal biological animals but refers to people who think, speak & behave like animals.

Similarly, the word "human" ("manussa") does not refer to all people but only refers to people with a "humane" (moral/ethical) mind. The suttas say:

Bhikkhus, a god, a human or any other good state would not be evident from actions born of greed, hate and delusion. Yet, bhikkhus, from actions born of greed, hate and delusion a hellish being, an animal birth a ghostly birth or some other bad state would be evident.

AN 6.39

Thus the suttas say:

the beings who fall away/shift/move (cutā) from humans and re-appear again as humans or gods are few, while those who fall away as humans and re-appear in hell, or the animal realm, or the ghost realm are many... It’s because they haven’t seen the four noble truths.

DD translation above from the links below:

https://suttacentral.net/sn56.102/en/sujato

to

https://suttacentral.net/sn56.131/en/sujato

The above appears to mean while people can be human (moral; ethical) during this lifetime, because they have not realised the Four Noble Truths, they can fall into the lower realms when alteration, loss, aging, death, etc, occur.

For example, I knew a devout Christian lady who was the most kind, moral & pure-hearted lady/mother one is ever likely to meet. She was an angel. But when her soulmate husband died, she mostly lost her mind and became often irrational. She fell away from angels & humans and re-appeared in the animal world. Even her own son, who is very highly spiritually developed (a 'god'), often cannot talk sense to her.

It follows there is no evidence for biological "rebirth". The writings of Pa-Auk Tawya Sayadaw appear to be illogical tiracchāna katha.

The first is that i believe that there is a powerful continuity between rebirths. So my personnal and subjective understanding is that when we look at a person, we can easily guess what type of person he was in a previous birth.

While there is no evidence for life-to-life rebirth, yes, your theory above is logical.

Animals are described as experiencing mostly greed, hatred, delusion.

Yes. Correct.

I think this is seriously off.

The Buddha exhorted his followers to reflect deeply about the teachings to the point of visible here-&-now realisation (rather than merely accept on blind faith).

Animals are instinct driven and regularly obey their instincts

Correct. This is why they are classed as "animals" and why people who are similar are classed as "animals".

but many of them are often peaceful and detached.

The above is irrelevant. The peaceful detached animals are still controlled by instinct rather than by objective human reason, wisdom & intelligence.

Many animals are peaceful and worry-free, even though their lives are harsh and short. Turtles are another example of a peaceful animal which can live longer than humans.

As already suggested, the above irrelevant. Docile animals still lack objective human consciousness that can observe the mind's own drives, instincts & motivations without acting upon them. Unlike humans, an animal cannot rationalize an ethical framework towards its potential range of behaviors and their consequences.

Would experienced buddhists agree with the passage quoted, and if yes, what arguments would they provide to change my analysis?

I already posted I do not agree with the superstition of Pa-Auk Tawya Sayadaw. The various realms in Buddhism represent the behaviour of people. People can behave, either occasionally or habitually, in a human, benevolent godly, demonic godly, animal, ghostly or hellish manner.

The majority of moral people (humans) will be 'reborn' in hell when death occurs to their loved ones or approaches themselves.

Then the Exalted One,
taking up a little dust
on the tip of his finger-nail,
said to the monks:

"Now what think ye, monks?

Which is the greater,
this little dust I have taken up
on the tip of my finger-nail,
or this mighty earth?"

"Greater, lord, is this mighty earth.

Exceeding small
is this little dust taken up
on the tip of the Exalted One's fingernail:
it cannot be reckoned,
it cannot be compared therewith.

It does not come to the merest fraction
of a part of it
when set beside the mighty earth, -
this little dust taken up
on the tip of the Exalted One's finger-nail."

"Just so, monks,
few are those beings that are reborn among men:
more numerous are these beings
that are reborn other than men.

What is the cause of that?

It is through not seeing four Ariyan truths.

What four?

The Ariyan truth of Ill,
the Ariyan truth of the arising of Ill,
the Ariyan truth of the ceasing of Ill,
the Ariyan truth of the practice that leads to the ceasing of Ill.

Wherefore, monks, an effort must be made to realize:

'This is Ill'.

'This is the arising of Ill.'

'This is the ceasing of Ill.'

This is the practice that leads to the ceasing of Ill.'"

—http://buddhadust.net/dhamma-vinaya/pts/sn/05_mv/sn05.56.061-070.wood.pts.htm

and the suttas that follow.