compose: Refactor some logic; implement redesigned error banner

[chrisbobbe]

Prompted by reviewing Zixuan's #924, this is meant to make the compose-box code better prepared for that work than it is in main; details at https://github.com/zulip/zulip-flutter/pull/924#pullrequestreview-2450028109 and in the commits.

Please let me know as soon as anything doesn't look clear. I'm tired (it's almost bedtime 🙂) but I've spent a while on this and I wanted to get it in today if possible. Since this makes a UI change, screenshots coming soon.

Fixes: #1089

[chrisbobbe]

main	#924 (revision at 01c91ce50)	This PR