Drop Compat dependency + Update CI

[carstenbauer]

IMO, it is not worth it just for the public keyword. We can use the recommendation from https://docs.julialang.org/en/v1.12-dev/manual/modules/#Export-lists instead.

[codecov-commenter]

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.27%. Comparing base (eb1e0a6) to head (594c06e).
Report is 7 commits behind head on main.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main      #44      +/-   ##
==========================================
+ Coverage   94.00%   95.27%   +1.27%     
==========================================
  Files           2        2              
  Lines         250      233      -17     
==========================================
- Hits          235      222      -13     
+ Misses         15       11       -4     

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[carstenbauer]

I've updated the CI config to now test lts, the latest 1.x release, and pre.