add Actions badges to README, correct existing badge and link

[digital-carver]

The link to the Stable docs had text and badge saying "Docs Latest" which usually refers to dev docs in Julialand, so changed the text and badge to "Docs Stable" instead.

Added badges to track the UnitTests and Downstream CI actions.

The "read the documentation" link was pointing to https://biojulia.dev/Automa.jl/latest/ which seems to be some old version of the documentation (before dev docs started being under /dev/), changed that to /stable/.

[jakobnissen]

Thanks for picking this up!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (82a27f0) 95.92% compared to head (61da004) 96.15%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #131      +/-   ##
==========================================
+ Coverage   95.92%   96.15%   +0.22%     
==========================================
  Files          16       16              
  Lines        1793     1793              
==========================================
+ Hits         1720     1724       +4     
+ Misses         73       69       -4     

Flag	Coverage Δ
unittests	96.15% <ø> (+0.22%)	⬆️

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see 1 file with indirect coverage changes

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