Prevent default ErrorHandler self-delegation

[MrAlias]

Fix #5135

• Follow the pattern used for all other global state.
• Self contain delegation to the ErrDelegator type and therefore remove the unneeded ErrLogger type.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.7%. Comparing base (98fd439) to head (57bd075).

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #5137     +/-   ##
=======================================
- Coverage   83.7%   83.7%   -0.1%     
=======================================
  Files        252     252             
  Lines      16450   16458      +8     
=======================================
+ Hits       13772   13778      +6     
- Misses      2387    2389      +2     
  Partials     291     291             

Files	Coverage Δ
handler.go	100.0% <100.0%> (ø)
internal/global/handler.go	100.0% <100.0%> (ø)
internal/global/state.go	100.0% <100.0%> (ø)

... and 1 file with indirect coverage changes