Add several updates for bitrot and QA improvements

[jlapeyre]

Updates for bitrot, add many tests, QA, and CI improvements

• Try to fix badge links in README
• Update CompatHelper.yml
• Update Aqua test for newer Aqua API
• Fix Aqua complaints in Project.toml
• Restrict some input types to Integer
  These are always integers anyway
• Fix JET complaint
  Seems to have a problem with log(::Complex) in general. Looks
  like a bug, if so. We don't really fix it, but rather skip it.
• Don't test nightly on CI because it's broke with JET
• Remove non-API function for input z == MathConstant.e
  The removed function has an underscore prefix and is not called at all by the
  API function lambertw.
  This non-API function returns 1::Int, which makes no sense. If you convert z to Float64,
  then 1.0::Float64 is returned, which is just as much exactly one as 1::Int.
  The API function intercepts the input ::MathConstant.e and converts it to float
• Improve doc strings
  lambertw was is outdated
  Function for branchpoint is better documented.
• Remove special case for argument ::AbstractIrrational
  I don't see that this code path was called by the API in any case.
  But curiously, codecov showed that this line was in fact covered by the test suite.
  The test suite in fact still passes, as expected, with this line removed.
• Remove another obsolete code path for special inputs
• Integers and Rationals are converted to floats at the API entry point.
  The removed non-API functions would add nothing if they were called. In any case, they are not.
• Part of the code path for abs(z::Complex) <= one_t/convert(T, MathConstants.e) was not tested before.
  This commit adds a test
• Add tests for uncovered code paths
• Some paths for complex arguments were not tested. This adds tests
• A redundant logic test was removed from code in one of these paths.
• Test inverse functions
  I used finv(lambertw), but it was not tested. I tried promoting the
  idea, but didn't push hard and got no comments. There is now a package
  implementing this idea.
  In any case, this adds a test for the existing, unexported, function.
• Remove unnecessary type parameter in signature
• Simplify function signature
  I may have argued that the complicated one was slightly more performant.
  If it is, it is not significant.
• Remove unused loop variable
• Add tests for complex args to hit paths in branch point expansion
• Remove unneccesary use of local
• Remove another unused, and in any case, unneccesary code path
• Test string(Omega())
• Update codecov action
• Remove commented out cruft
• Rename unused loop var to underscore

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.39%. Comparing base (6b6e2c8) to head (f5f5645).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #31      +/-   ##
==========================================
+ Coverage   92.02%   99.39%   +7.36%     
==========================================
  Files           1        1              
  Lines         188      164      -24     
==========================================
- Hits          173      163      -10     
+ Misses         15        1      -14     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.