core: fix client-side only validation allowing admin to set blank user password (backport of #16467)

[authentik-automation]

⚠️ This cherry-pick has conflicts that require manual resolution.

Cherry-pick of #16467 to version-2025.6 branch.

Original PR: #16467
Original Author: @BeryJu
Cherry-picked commit: 180cec9

Please resolve the conflicts in this PR before merging.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.94%. Comparing base (af9f124) to head (c71a98e).
⚠️ Report is 2 commits behind head on version-2025.6.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@               Coverage Diff               @@
##           version-2025.6   #16470   +/-   ##
===============================================
  Coverage           92.93%   92.94%           
===============================================
  Files                 817      817           
  Lines               42295    42304    +9     
===============================================
+ Hits                39308    39318   +10     
+ Misses               2987     2986    -1     

Flag	Coverage Δ
e2e	47.49% <20.00%> (-0.01%)	⬇️
integration	24.37% <20.00%> (+<0.01%)	⬆️
unit	90.84% <100.00%> (+<0.01%)	⬆️

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