Both auto-forwarding and auto-reply are paid features, which makes cancelling & switching much more difficult. Gmail is a breeze comparatively. I highly recommend against using their addresses (e.g. protonmail.com, proton.me, pm.me)
Email forwarding is available for everyone with a paid Proton Mail plan.
(source)
That’s the “special application” I mentioned, but it seems to have been updated since I last looked at it so it now offers the same level of encryption as the webmail app.
I would prefer to see it freely available, but it doesn’t seem foundational to using the service in any scenario - free accounts have the webmail and mobile clients, which are arguably both more flexible (and maintainable) than the Bridge.