CI: Build docker image on GHA

[effigies]

Trying to use GHCR as a cache.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 72.06%. Comparing base (52eee57) to head (c28707c).
Report is 65 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #3379   +/-   ##
=======================================
  Coverage   72.06%   72.06%           
=======================================
  Files          57       57           
  Lines        4231     4231           
  Branches      456      456           
=======================================
  Hits         3049     3049           
  Misses       1067     1067           
  Partials      115      115           

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[effigies]

buildx seems to be trying to push to a Docker registry as well, causing a crash.

docker/buildx#2731