Nextcloud isn't a email server and so doesn't contain any emails. However I presume you are talking about this mail client app? You wouldn't see this in the android client as that is only for the files stored in Nextcloud
If you wish to use the Nextcloud mail app on your phone you will have to log in with your browser. As the mail app is only an IMAP client you can just use any mobile native IMAP client to interface with whatever email server you are dealing with. I presume that's the hetzner server that has Nextcloud and an Email server set up for you to use
yes, if you set up a nextcloud installation (which will cover many of your other privacy bases), there is a addon (Mail) that is an email client that works like Thunderbird in that it accesses your other accounts via IMAP.
Have you considered using nextcloud? They are open-source and from what i have looked-up right now they seem to have E-Mail too (https://apps.nextcloud.com/apps/mail) Nextcloud offers 0retty much everything else too. They even have a tool to migrate all your data over from the google-suite so you dont have to take care of that :) And if you dont over 8 GB then its free (might work for email) Hope it helps
Sorry for not being more specific. I didn't know there was a choice! Just goes to show how healthy the nextcloud ecosystem is. Maybe it's the same client in the groupware, but I meant this one: https://apps.nextcloud.com/apps/mail