[extension/extensionauth] Deprecate methods on Func types

[mx-psi]

Description

Depends on #12478, deprecates methods that are unnecessary

[jade-guiton-dd]

Do you think this panic in contrib-tests is relevant? It looks to me like that test should have panicked even with the previous code however (creating an auth.NewClient() with no options should result in a segfault when trying to call the function, whether it's embedded or not)

[mx-psi]

Do you think this panic in contrib-tests is relevant? It looks to me like that test should have panicked even with the previous code however (creating an auth.NewClient() with no options should result in a segfault when trying to call the function, whether it's embedded or not)

I added the nil check present in the Func types: 38d366c. I think that should solve the panic, thanks for pointing this out

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.05%. Comparing base (58f3efb) to head (7d4cb15).
Report is 15 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #12480      +/-   ##
==========================================
- Coverage   92.16%   92.05%   -0.11%     
==========================================
  Files         465      467       +2     
  Lines       25201    25267      +66     
==========================================
+ Hits        23226    23260      +34     
- Misses       1576     1605      +29     
- Partials      399      402       +3     

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