I realize it would be a big lift to make Proton Calendar work seamlessly with every 3rd party calendar booking app out there. So if you can't prioritze TidyCal, then here are my suggestions in order of preference after this option:

(1) A user should be able to with a couple of clicks, add an ICS file attachment from an email to the Proton Calendar.

(2) A user should be able to upload an ICS file from inside the desktop and mobile apps. Currently this function is broken in both the web browser through the settings, and on the desktop app in settings.

I tested this, by the way. The same file uploaded to my google calendar works there but does not work in proton calendar.

I have a TidyCal lifetime subscription (via AppSumo) because it's easy and cheap. When someone submits a booking, I get an .ics file sent to my proton account. I would tolerate this level of clunky manual workaround intervention if it worked, but it doesn't work.

In settings ->Proton Calendar -> Import/export -> Import -> Import from ICS...
I get a generic error: "Import events. An error occurred reading your file "booking.ics". Incorrect file format."

TidyCal doesn't offer a direct connection with a protonmail account (not surprising) - https://tidycal.com/integrations/calendars.

But it does have an OAuth API option with personal access tokens and OAuth Clients.
https://tidycal.com/integrations/advanced
https://tidycal.com/integrations/oauth.
So perhaps that could be an option if Protonmail allowed for OAuth integrations.

I expect for $10/month this basic functionality should be working, and maybe even easy and automated.