sequential queueing of cells not working

I'm having issues similar to #5098 #4825 and #6794 which are all unresolved.

- Jupyter version 6.5.4
- OS: ubuntu 20.04

When i first run cells in a new notebook, new environment with just python3.9 and ipykernel, things work fine.

But if I try to queue up some more cells, only the first one runs.

Notice the "executed in 0ms" messages after trying to run those cells.

In the jupyter console I get these "Kernel does not exist" messages, not sure if it is related or not:

```
[I 15:02:27.694 NotebookApp] Starting buffering for 9216ccef-4201-4342-bc52-a028f811bfca:b304d623d91440c28393f63ec065f24e
[I 15:02:27.936 NotebookApp] Kernel restarted: 9216ccef-4201-4342-bc52-a028f811bfca
[I 15:02:27.955 NotebookApp] Restoring connection for 9216ccef-4201-4342-bc52-a028f811bfca:b304d623d91440c28393f63ec065f24e
CONDA_PREFIX=/home/aolab/miniconda3/envs/jupyter-test
[I 15:02:28.959 NotebookApp] Replaying 3 buffered messages
[W 15:02:36.955 NotebookApp] 404 GET /api/kernels/10e459da-d08b-49dc-a304-fe18f07016aa/channels?session_id=965d2597cca643449e915aff27ecf6b6 (128.95.205.111): Kernel does not exist: 10e459da-d08b-49dc-a304-fe18f07016aa
[W 15:02:36.956 NotebookApp] 404 GET /api/kernels/10e459da-d08b-49dc-a304-fe18f07016aa/channels?session_id=965d2597cca643449e915aff27ecf6b6 (128.95.205.111) 2.120000ms referer=None
```

This wasn't a problem until about a month ago when it started happening all the time. Don't know what changed. Tried updating notebook and ipykernel but neither made a difference.

Reproduce the failure in Jupyter Notebook 6.5.4 on Ubuntu 20.04 by running several cells and checking whether only the first executes. Start by comparing the notebook's queued-cell behavior with the kernel restart and "Kernel does not exist" log messages; done means queued cells execute sequentially without the reported 0ms results or kernel errors.

Written by the indexing model from the issue text.