Health indicators that take a long time to respond are difficult to diagnose

[philwebb]

See #4391 (comment) for background.

It's currently very hard to tell if health indicator will cause a web request timeout as logging only occurs on error. We could offer an option to log health indicators that take a long time to respond.

[philwebb]

See also #25459

[philwebb]

This could be considered a usability bug and something we could address in 2.x

[wilkinsona]

I think we should aim to fix this in 2.6.x. If the changes to improve the diagnostics are too risky for the stage we're at in 2.6.x's maintenance, we can always push it out to 2.7.x again.