My manager messages at 11pm and I feel like I have to answer

The important detail here is that this has never been stated in either direction. You are following a rule nobody wrote, which means you're carrying the full cost of it and getting none of the credit for compliance.

First, test the assumption rather than the anxiety. You believe fast repliers get better projects. That might be true, or it might be that the fast repliers are also senior, or in his time zone. Before you reorganise your sleep around it, look at who actually got the last three good projects and when they typically reply.

Second, make the norm explicit, and let him be the good guy. Time-zone-split managers usually have no idea what time their messages land, and most are genuinely relieved to say so:

"Your messages often reach me around 11pm. I'd rather pick them up first thing than reply half-asleep, is that fine? And if something is ever genuinely time-critical, call me and I'll answer."

This costs him nothing to agree to, and once he's said yes, the unwritten rule is written and it's on your side.

Third, remove the physical mechanism. Sign out of chat on your phone, not notifications off, signed out. The habit is doing more damage than the messages, and willpower at 11pm is not a plan.

If he does expect replies at 11pm, you now know something concrete about the job rather than something vague about yourself. That's a conversation about scope and coverage, and possibly a conversation about whether the role is survivable, but at least it's the real one.

General perspective from remote work experience, not HR or legal advice.