Does Proton Bridge also syncs the calendars?

If I understood correctly, Proton Bridge can be used to sync the Email with IMAP and SMTP with a local mail client like Thunderbird, Evolution, Geary, Kmail, etc.
Does it also syncs the calendar? What I mean is, can I have my Proton Calendar displayed in my local calendar app (in my case GNOME Calendar) and intergrated with the system, so that I can see the upcoming events in the calendar widget of the system panel?

That could be a deciding factor for me when it comes to choosing between Tutanota and Proton as the paid Email and Calendar service I will use. Both have apps that are good enough for Android (although a widget for the Tutanota calendar would be nice) while on the desktop Tutanota as an app that doesn’t integrate at all with the system and Proton as nothing other than webapps and Bridge.

Afaik, Proton still doesn’t offer CalDAV support, so there’s no way to sync Proton Calendar with Thunderbird and etc. officially.

But there are plans for a Proton Mail desktop app, as announced in the road map.

Relevant part:

Finally, we’re experimenting with an Electron.js desktop app to take Proton Mail beyond the browser for Mac, Linux, and Windows. We’re still in the early stages, and we don’t have a beta or general release timeline just yet. But we know that a desktop app is high on the wishlist for many of you, so we thought you’d like to know it’s on our radar.

I’m not entirely sure if that desktop app will also allow users to use Proton Calendar (like the Tutanota desktop app), but I would imagine the probability is high.

If the Proton Map desktop app comes out, it’ll be Electron-based just like the Tutanota desktop app, so there won’t be much differences in terms of offerings between the two, for your purposes.