Protonmail is fine for searching old emails and they have their own calendar integration. I self host calDAV for my own calendar so I cannot comment on protonmail's other cloud services but I'm happy enough with their email service that I subscribe yearly for it.
That's the downside of not getting data mined, you need to pay for these services. Setting up a private cloud is not impossible for a derp like me but a private email server is definitely well beyond my skillset so that's something I pay for.