Ramp up priority of the sql_connection_string, if set.

[niklassiemer]

closes #1904

[codecov]

Codecov Report

❌ Patch coverage is 85.18519% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 80.37%. Comparing base (4c8fd55) to head (ed7ec61).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
pyiron_base/database/manager.py	60.00%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1954      +/-   ##
==========================================
+ Coverage   80.34%   80.37%   +0.02%     
==========================================
  Files          79       79              
  Lines       10458    10462       +4     
==========================================
+ Hits         8403     8409       +6     
+ Misses       2055     2053       -2     

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