Remove hardcoded client install

[blink1073]

Follow up to #988

[codecov-commenter]

Codecov Report

Base: 72.60% // Head: 72.54% // Decreases project coverage by -0.06% ⚠️

Coverage data is based on head (0679984) compared to base (c88846c).
Patch has no changes to coverable lines.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #991      +/-   ##
==========================================
- Coverage   72.60%   72.54%   -0.07%     
==========================================
  Files          64       64              
  Lines        8243     8243              
  Branches     1378     1378              
==========================================
- Hits         5985     5980       -5     
- Misses       1844     1848       +4     
- Partials      414      415       +1     

Impacted Files	Coverage Δ
jupyter_server/services/kernels/handlers.py	57.68% <0.00%> (-1.06%)	⬇️

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