Use DOCUMENTER_KEY to deploy docs

[odow]

Actions which use GITHUB_TOKEN can't themselves trigger new actions:
https://docs.github.com/en/actions/using-workflows/triggering-a-workflow#triggering-a-workflow-from-a-workflow

So if we upload the docs with GITHUB_TOKEN, it doesn't then trigger the push notification for the deploy-static action.

[codecov]

Codecov Report

Patch and project coverage have no change.

Comparison is base (2a1c402) 92.71% compared to head (7ba39f6) 92.71%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #670   +/-   ##
=======================================
  Coverage   92.71%   92.71%           
=======================================
  Files          27       27           
  Lines        3334     3334           
=======================================
  Hits         3091     3091           
  Misses        243      243           

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