fix(fastapi): do not read request body for fastapi_mcp

[alexander-alderman-webb]

Calling request.json() reads the request body, and nothing is left in the receive callable that fastapi_mcp passes to the mcp package to read the request.

The fix involves checking if we have a fastapi_mcp endpoint. If so, do not read the request body.

Closes #4764

[codecov]

Codecov Report

❌ Patch coverage is 55.55556% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.52%. Comparing base (94a92d8) to head (56ec01c).
⚠️ Report is 10 commits behind head on master.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
sentry_sdk/integrations/fastapi.py	66.66%	1 Missing and 1 partial ⚠️
sentry_sdk/integrations/starlette.py	33.33%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4794      +/-   ##
==========================================
- Coverage   84.55%   84.52%   -0.03%     
==========================================
  Files         158      158              
  Lines       16479    16513      +34     
  Branches     2855     2867      +12     
==========================================
+ Hits        13933    13957      +24     
- Misses       1700     1703       +3     
- Partials      846      853       +7     

Files with missing lines	Coverage Δ
sentry_sdk/integrations/fastapi.py	87.35% <66.66%> (-1.67%)	⬇️
sentry_sdk/integrations/starlette.py	84.55% <33.33%> (-0.48%)	⬇️

... and 16 files with indirect coverage changes