New websocket unable to communicate with kernel paused in debugging

[kycutler]

Description

When establishing a new websocket connection to a kernel whose execution is paused due to debugging (e.g. paused on a breakpoint), messages sent over the websocket get no reply -- including debug requests.

Reproduce

1. Connect to a kernel that supports debugging (e.g. IPyKernel >= 6)
2. Set a breakpoint in the kernel (e.g. using JupyterLab) and run the code so that execution is paused
3. Open a new websocket connection to the kernel
4. Notice that the websocket gets no responses, even from messages over the control channel.

Seems to be causing jupyterlab/jupyterlab#10174.

Tested against different versions of jupyter_server and traced the issue back to version 1.1.2 (the issue does not repro in 1.1.1). This correlates with #361. While in this "frozen" state the console also shows that the server is nudging the kernel repeatedly, so it makes sense if this is the cause.

Expected behavior

The kernel should still be able to communicate, at least over the control channel so that frontends can continue the debugger and unblock the shell.

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[JohanMabille]

Fixing this requires to modify the protocol, I'm going to open a JEP for that.