Make websocket handshake failures to transparently report server-responded error information

[achimnol]

WIP.

[codecov]

Codecov Report

Patch coverage: 66.66% and project coverage change: -1.51 ⚠️

Comparison is base (d2669a0) 43.01% compared to head (cda348b) 41.51%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #81      +/-   ##
==========================================
- Coverage   43.01%   41.51%   -1.51%     
==========================================
  Files          50       50              
  Lines        5145     5001     -144     
==========================================
- Hits         2213     2076     -137     
+ Misses       2932     2925       -7     

Impacted Files	Coverage Δ
src/ai/backend/client/request.py	68.43% <66.66%> (+0.97%)	⬆️

... and 32 files with indirect coverage changes

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