feat: use cached request session when fetching schedule

[jooola]

Description

This should prevent a big amount of duplicate calls against the API, for the same show or show instance data.

[codecov]

Codecov Report

Attention: Patch coverage is 63.41463% with 15 lines in your changes are missing coverage. Please review.

Project coverage is 49.39%. Comparing base (2b119ad) to head (9c7e371).
Report is 41 commits behind head on main.

Files	Patch %	Lines
api-client/libretime_api_client/_client.py	40.00%	15 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #2989       +/-   ##
===========================================
- Coverage   70.36%   49.39%   -20.98%     
===========================================
  Files         149       26      -123     
  Lines        4033     1559     -2474     
===========================================
- Hits         2838      770     -2068     
+ Misses       1195      789      -406     

Flag	Coverage Δ
analyzer	?
api	?
api-client	61.08% <40.00%> (-3.33%)	⬇️
playout	47.64% <100.00%> (+0.23%)	⬆️
shared	?
worker	?

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.