Consent is more objective than sanity, although there are edge cases:

Suppose a 16-year-old agrees to have sex. Is that consent?

Where I live 16-year-olds can legally have sex! Anyway, assuming things are different where you live, then yes, they can give consent, but their consent does not legally authorise sex.

If a contract is made under "undue influence," did I consent to it? Is that objective? If my agreement is made under coercion, did I consent? What counts (morally) as coercion seems very fraught. Leftists and feminists frequently argue that many seemingly voluntary activities are actually deeply coercive, and use terms like "wage slavery."

Well, yes you did consent. This doen't necessary make everything ok, and it might be better if there was less coersion, but you still consented.

Suppose I agree to an act, then change my mind later. If the other person carries out the act anyway, did I consent to it? In law, and in most people's intuition, the answer is "it depends."

You consented, and then withdrew your consent. If the other person carries out the act before you withdraw consent, then they can't be blamed.

All in all, it looks very much like "communicated agreement" is the objective fact, and whether that gets upgraded to "consent" depends on a whole host of ethical judgments that are often contentious.

I'd say "communicated agreement" is consent by definition. Its possibly a word getting a little overloaded : the word consent can be used as in "Russia consented to hand over 1/4 of her territory to Germany" or as in "Let's have sex!" while these are rather different in most important respects.