Add support for custom private image tags

[simonmarty]

Issue #, if available:

Description of changes: #539 updated the PRIVREPO env var to support appending tags to the private image repo. This conflicts with our release makefile.

Extract the image tag to a separate env var.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 61.56%. Comparing base (f0808bf) to head (89cc5cc).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #558   +/-   ##
=======================================
  Coverage   61.56%   61.56%           
=======================================
  Files          11       11           
  Lines         752      752           
=======================================
  Hits          463      463           
  Misses        274      274           
  Partials       15       15           

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