How to restore just an IMAP email account's Inbox folder in TimeMachine

Continuing, since I had important email in my Gmail account that was deleted, I next restored all my email folders. With my network connection still off, I opened Mail and got:

"There is a problem with your mailboxes.

Try clicking Quit and then opening Mail again. If this message reappears, click Quit and Rebuild index. The next time you open Mail, it will import your messages.

[two buttons:] Quit Quit and Rebuild inboxes"

Quit didn't solve the problem, so I chose: "Quit and Rebuild inboxes"

I opened Mail, and perhaps all the mail in my inbox that had been deleted was now showing. Yay! Sort of. Once I reestablished the network connection, the server inbox became master and deleted all the messages that I previously deleted and then restored. Perhaps I should repeat the restore with the network connection off, and move the inbox message to a mail subfolder I create, since mail subfolders don't seem to have the problem with the mail server overwriting them.

For my Gmail account, only a handful of messages in my inbox were showing, even after turning on the network connection. I don't know why I was not able to restore the Gmail inbox deleted messages.

I decided to try restoring from Time Machine, with Mail not running. I initially restored the 32 char string folder at the same level as my self-created folders, but the inbox contents did not change. Then I restored the entire account ~/Library/Mail/V9/E3A9C34E-ADFD-463D-92C6-FC061A06XXXX . The inbox contents did not change. I figured there was a chance the account was syncing to the mail server and more or less immediately overwriting what I restored, so I repeated the restore and viewing of the inbox with the network connection (wifi) off, but the inbox still did not change.

Side note: Apple's support doc for macOS 12 says to rebuild a mailbox, "…select a mailbox in the sidebar. Choose Mailbox > Rebuild" There is no such option. But even if there were, it wouldn't be viable for my IMAP account because: "When you rebuild mailboxes for IMAP or Exchange accounts, messages and attachments stored on your Mac are discarded, and then downloaded again from the mail server to your Mac."

I discovered that besides restoring my account folder with my network connection off, I also had to restore the MailData folder at the same level as my mail store (which did occur when I restored all folders in ~/Library/Mail/V9/E3A9C34E-ADFD-463D-92C6-FC061A06XXXX. Then my inbox messages that had been deleted appeared. However once I connected to the network, the server inbox became master and deleted all the previously deleted inbox messages. I repeated the restores; moved all the inbox messages to a mail folder I created, but after reconnecting to the network, the messages in the folder I placed my inbox messages in goes to count 0 after a bit of time. Odd, because other folders I created at the same level (which apparently never had any messages deleted) still show messages.

I also l need a solution for restoring my Gmail inbox, because that isn't working; not even a temporary showing of previously deleted inbox messages.

At least a *bit* of hope for the Gmail account anyway: After restoring the Gmail and MailData folders, it appears the deleted inbox messages now are stored in Archive, and have not been deleted after turning on the network connection. Not ideal, but I can work with it.

Super helpful; thanks. Do you think once in Archive they remain there (unless deleted manually), or might they auto delete after 30 days or something?