need help with apple mail

My Apple Mail program (which I've happily used since, like, forever) is behaving erratically and I'm concerned about the increasing frequency of this behavior. I'm using Apple Mail version 16.0 (3731.400.51.1.1) on an iMac using Ventura 13.2.1. What is happening is this:

1) From time to time I'll attempt to delete one or more messages in my inbox and nothing happens. I give it a couple of tries, then quit the Mail program.

2) Often (though not always), this action does allow the messages to be deleted, but

3) Every time I've quit the program in this context and returned to it, suddenly several of my "sent" messages will appear in my inbox (sort of replacing the deleted messages).

I don't use a lot of Rules so I'm constantly moving stuff out of my inbox. I can't see how that would affect this strange sequence of events.

This is happening with increasing frequency—now it's happening three to five times a week. And as of two weeks ago, the steps I have taken to "fix" the situation aren't always working.

I would appreciate any insights/help. Thank you in advance.