Use the rich library for logging (alt)

[serhiy-storchaka]

Closes #1887.

This attempt uses the hand-made handler instead of RichHandler (as in #1897) and works after closing sys.stderr. The output is closer to the xurrent output, but prefixes like "ERROR: " are output also in no-color mode.

Also fixed logging for CRITICAL errors (it now contains red prefix as for ERROR).

[codecov]

Codecov Report

Merging #1907 (b7e3b65) into master (b26de62) will decrease coverage by 0.00%.
The diff coverage is 82.85%.

@@            Coverage Diff             @@
##           master    #1907      +/-   ##
==========================================
- Coverage   86.39%   86.38%   -0.01%     
==========================================
  Files          60       60              
  Lines        9386     9389       +3     
  Branches     1468     1469       +1     
==========================================
+ Hits         8109     8111       +2     
- Misses       1004     1007       +3     
+ Partials      273      271       -2     

Flag	Coverage Δ
cli	64.89% <77.14%> (+0.01%)	⬆️
e2e	65.60% <77.14%> (+0.06%)	⬆️
sdk	89.33% <ø> (ø)

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Impacted Files	Coverage Δ
neuro-cli/src/neuro_cli/main.py	73.75% <70.00%> (+0.14%)	⬆️
neuro-cli/src/neuro_cli/log_formatter.py	89.28% <88.00%> (+6.67%)	⬆️
neuro-cli/src/neuro_cli/asyncio_utils.py	76.82% <0.00%> (-0.67%)	⬇️
neuro-cli/src/neuro_cli/ael.py	49.23% <0.00%> (-0.51%)	⬇️

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[asvetlov]

LGTM, please merge