Explore solutions for codecov upload failures

[RMeli]

As reported in #4574, codecov often fails to upload reports from a fork. PR #4575 removed the CI failure for codecov uploads, which is not an ideal long-term solution.

This issue is to track possible long-term solutions. As stated in #4574 (comment):

Longer term - if nothing happens within codecov by end of May, then we should take the time to review the pro/cons of alternate providers and see which is best to move from.