@Rowan
Out of interest are you experiencing this issue when sending messages via a Gmail Account?
I've noticed this problem myself when using both Windows 11 & 10. Mostly this issue happens with my Gmail account and the solution is not an easy one. Repairing the Mail app always fails to resolve this issue, as does uninstalling and reinstalling it. To be honest I've raised so many reports with Microsoft about the various issues with the Mail app that I think it fair to say it's still an unfinished project. I read a long time ago that the app was originally designed for mobile users hence why it's not so feature-rich and this has been criticised by many users of the desktop product. Below is a list of issues I sometimes experience and have done so for quite some time.
1. Mail app often reports a problem with one of my accounts, usually the Gmail one!
2. Sent messages sometimes appear twice in the 'Conversation View' of my inbox - one message will often appear corrupted and capitalized.
3. Draught messages cannot be sent (as you mentioned).
4. Windows Dark Theme sometimes reverts to the default scheme when typing an email.
5. Windows Mail sometimes quits unexpectedly whilst typing an email.
I'm sure there are more issues, but I don't remember them all. With that said however most of these are extremely rare events these days. My situation has certainly improved since installing Windows 11. I have run the Windows command line tool 'sfc /scannow ' most times when these issues arise but to no avail. Often it seems the problems can be temporarily resolved by removing the mail account and then adding it back again though this might not be for everyone and it really depends on whether you're using a POP3 account or IMAP. I find it better to use IMAP if you want your emails to be restored from the server.
Probably not much help to you sadly, but you're not alone. These things are sent to try our patience and no doubt teach us new tricks.