/e/ has a Docker image on their TODO-list, which should enable you to self-host your data in an easy way:
we will provide /e/ services packaged as Docker images so that users can install the service on their own servers for self-hosting their mail, online storage, calendar etc.
So they already plan the functionality, that one can self-host ones own data.
Currently some data can only be synced with ones eDrive account, but I assume that this restriction will be extended in the future to support self-hosted servers.
Syncing contacts and calender can already be done with any CalDAV/CardDAV server of your choice. (I already use my own NextCloud server for that)
For messages/apps data I am not aware of a planned functionality - is that not a functionality of each app?
If you can think of a specific enhancement, then you can submit a featurerequest here: https://gitlab.e.foundation/groups/e/-/issues.