Oof, this is a weird bug. We'll definitely fix it.

Came here to mention the "any key" confuses people, we had to start telling people to hit space, so thank you for identifying more keys which work! We are also mostly on Mac, so unsure about other OSes but I will see if I can gather more information.
This also explains some weirdness we've seen with terminals timing out seemingly too quickly.

Spoke with someone else and same issues on Windows. The working keys seem to be space, shift, alt, ctrl, and the windows key.

@spettinichi you are right I can reproduce it on Windows. Part 2 of the OP is a duplicate of #8547

Ahh thanks for linking that! I didn't realize there was already a separate ticket for Windows!

I encountered into this issue too on v0.27.3 and noticed that in addition to affecting other web terminals, if you close a web terminal while having some other workspace application open then it also seems to interfere with that application.

For example, the window for Android Studio via JetBrains Projector shows the following for a few seconds after you close a web terminal window:

After a few seconds, the workspace application stops showing that connection message and goes back to normal.

We're able to reproduce this consistently on some of our clients and are investigating!