Murcielago GrapheneOS MTE usage does not always show the user an error notification, it silently terminates the app in some cases. It was observed by several Mullvad users before they deployed a new version of the app with a security fix that was possibly relevant. Also been observed by several Proton users of their apps and other apps. OP's reports are consistent with other reports. The question is which app versions the OP is running, which is relevant if one is to determine whether or not the bugs persist in newest versions.
Murcielago I briefly downloaded the Proton Mail App from Play store, tested it and it works fine without crashes and Memory tagging enabled.
Keep in mind that memory corruption bugs – or any bug – might not be triggerable from simply installing and using the app for a brief time. With respect, that's not enough to conclude that "it works fine" with memory tagging. It could be triggered by certain actions performed in the app. Or something. Other Proton users have reported issues when some of their apps are run with memory tagging, some have not (and then wrongly concluded that, since they're not experiencing issues, then there are no issues).