Meaning of "must have" as a modal

[Woods]

I have a doubt here: if you say "You must have been aware of the circumstances," does that mean that the person would have known about the circumstances, or that they had an obligation to know like in the present, or it could be both?

I ended up using "you should have known" instead because it's clear it states an obligation, even though I would have used "must have" if it was stronger, but wasn't introducing a doubt about whether they knew or not.

[linguoboy]

I have a doubt here: if you say "You must have been aware of the circumstances," does that mean that the person would have known about the circumstances, or that they had an obligation to know like in the present, or it could be both?

It’s purely epistemic: You’re saying it’s not possible the person could not have known.

I ended up using "you should have known" instead because it's clear it states an obligation, even though I would have used "must have" if it was stronger, but wasn't introducing a doubt about whether they knew or not.

“Should have” to me clearly expresses an obligation but implies they did not know. I can’t think of a single modal expression which conveys both.

[Woods]

What about those:

"I might have forgotten."
"I might forget."

I think the first applies to the present only - meaning that I most likely did forget, possibly not, but either way it's already a fact. The second applies to the future.

I am looking for one where I mean that I could forget but didn't (like I'm going out of the restaurant and was about to leave without paying, but at the last moment I realised that and paid). So what about "I could forget." - it seems to me that this one also applies mostly to the future, but maybe it could be used for something in the past as well? Or not? And is there one that applies only to the past? I guess "I was about to forget" or "I almost forgot" would be the closest - we can't really use a modal verb like can or might?

[linguoboy]

What about those:

"I might have forgotten."
"I might forget."

I think the first applies to the present only - meaning that I most likely did forget, possibly not, but either way it's already a fact. The second applies to the future.

Or the past: "I might have forgotten if he hadn't reminded me the next day." Both events occurred as some definite time in the past. The second can be past habitual (see below).

I am looking for one where I mean that I could forget but didn't (like I'm going out of the restaurant and was about to leave without paying, but at the last moment I realised that and paid). So what about "I could forget." - it seems to me that this one also applies mostly to the future, but maybe it could be used for something in the past as well? Or not?

Could can be conditional/irrealis or it can be past habitual, but it cannot be simple past.

So "I could forget, so I want you to remind me." Reference is to a possible event in the future, so irrealis.
"If I could forget, I would." Present conditional. (I can't forget, so this is hypothetical and counterfactual.)
"I could forget sometimes, so it was good that I had you there to remind me." Past habitual: Forgetting was something which occurred repeatedly during a closed period of time in the past.

But for a singular occasion where you were close to forgetting but it didn't happen you need the perfect: "I could have forgotten, but fortunately you were there to remind me."

And is there one that applies only to the past? I guess "I was about to forget" or "I almost forgot" would be the closest - we can't really use a modal verb like can or might?

See above. For habitual situations, you can use modals like could and might. For a single occasion, these need to be in a perfect construction.

[Woods]

Danke sehr