Transfer mailbox from Titan mail to iCloud+ Custom Email Domain

Hello everyone, I would like to ask for some advice.

What’s the situation?

I am currently using my own domain and TITAN mail. Since I have the iCloud+ service and the option to activate a Custom Email Domain, I am interested in the least painful way to handle this transfer.

My TITAN mail annual subscription expires at the beginning of October, so when and how should I do the transfer? I want to emphasize at the outset that I want to save the entire mailbox database, this is my main focus.

Since I would like to use the email with the predefined domain and the email I am currently using, is it wise to do the transfer now and choose the option to use the parameters from TITAN Mail, or should I wait for my subscription to expire and then choose the option to transfer to the Custom Email Domain without using the existing email? Again, I emphasize that I need to save the mailbox database. Also, I do not use Apple Mail as my primary email client; does that have any impact? Or am I required to use Apple Mail for the Custom Email Domain? I am currently using the Canary Mail client.

Since the situation is a bit complicated, I hope I have explained what I specifically want. Can someone give me advice?