If you use GnuPG or one of the GUI implementations it does.
No, because it’s the server that terminates the TLS connection, not the recipient’s client. TLS is purely a security control to protect the transport between you and the server you are talking to. It doesn’t have anything to do with e2ee. It’s still important, of course, but not for e2ee.
You do realize e2ee merely means that two users share public keys when they communicate in order to decrypt the messages they receive, right?
And how does TLS between you and your mail server help with this? Does it give you any guarantee that the public key was not tampered when it reached your server? Or instead you use the fingerprint, generally transmitted through another medium to verify that?
Nothing to stop you from hosting your own on an encrypted drive.
An encrypted drive is useful only when the server is off against physical attacks. While the server is powered on (which is when it gets breached - not considering physical attacks) the data is still in clear.
EteSync does E2E already
And…it requires a specialized client anyway. In fact, they built a DAV bridge (https://github.com/etesync/etesync-dav). Now tell me, if you use this on -say- your phone, can you use other DAV tools without using such bridge? No, because it does something very similar to what Proton does. If proton bridge will get calendar/contacts functionality too (if, because I have no idea how popular of a FR it is), you are in the exact same situation.
I went to look for the video and somehow was worse than I had imagined.