Can anyone tell me the standard for determining if a mouse is depressed? Or anxious? Just curious

Or tripping? I think that we can ascertain some things from their physiological responses, eg fear, anxiety and being content. Obviously there’s a lot we don’t know about their internal state. Psychedelics really need to be tested on humans.

What scientifically credible, i.e. at least stably reproducible, connection does the head twitch response in mice have to do with depression in humans?

The head twitch test is used to determine whether a substance activates 5HT2A in the same way psychedelics do.

The forced swim test is used in animal models of depression: https://en.m.wikipedia.org/wiki/Behavioural_despair_test

I'm a layman, I don't know what the scientific basis is for using the test to model depression. I personally find it pretty cruel.

There is nothing credible.

This research direction is an example of "cargo-cult science" [1] as Feynman understands the term. (That does not mean that the hypothesis is necessarily wrong.) There is a reason for "in mice" being an internet meme [2].

[1] https://calteches.library.caltech.edu/51/2/CargoCult.htm

[2] https://nitter.eu/justsaysinmice

Look up the forced swim test.