It's actually fairly simple: if the server never has access to the keys or the plaintext of messages (or calendar events, etc.), then you need a client tool to handle decryption and encryption operations.
They use PGP, and they have implemented this feature in a way that it's completely transparent to the user to make it mainstream. So they chose building dedicated tools (bridge, web client), rather than letting users use their own tools, because the PGP tooling sucks hard and it's extremely inaccessible for the general population.
This means that you need a fat client, whatever you do, or otherwise the server will have access to the data and there is no e2ee. Instead of using enigmail or other PGP plugins/tools, they built the bridge.