ProtonMail doesn't support IMAP without running a background bridge/converter, only their HTTP API, so on mobile you have to use their firstparty app, not the native OS email client on the mobile device. this is fine.
however, their 1p email client doesn't let you sort a mailbox, or select multiple items and move them all to archive or a folder. unsorted, one by one. ugh.
@kzimmermann protonmail bridge is free software and is open source, and you can use it with any IMAP client you like. additionally, their mobile clients are all open source. you're barking up the wrong tree.