analyze didn't return it because it's not configured to run on the bot at all. Is that something we ought to change?

Yes, I think so.
media_unittest runs on buildbots, so I think we run it on try bots as well (and probably all other tests that run on the Fuchsia build bot).

How was the current set of tests to run selected? It doesn't seem right to run content_unittests, but not media_unittests.

Which buildbots do you mean?

The tests run by both chromium.linux:Fuchsia x64 and tryserver.chromium.linux:fuchsia_x64 are configured here: https://codesearch.chromium.org/chromium/src/testing/buildbot/chromium.linux.json?rcl=c4dd10518c291c20a9881e6720d8b9a9505c2010&l=391

The tests run by chromium.fyi:Fuchsia (which may be the bot you have in mind?) are configured here: https://codesearch.chromium.org/chromium/src/testing/buildbot/chromium.fyi.json?rcl=c4dd10518c291c20a9881e6720d8b9a9505c2010&l=3626

We didn't have it on trybots as it was still flaking regularly on the fyi waterfall. Looking through recent history I see

https://ci.chromium.org/buildbot/chromium.fyi/Fuchsia/12116
https://ci.chromium.org/buildbot/chromium.fyi/Fuchsia/12001
https://ci.chromium.org/buildbot/chromium.fyi/Fuchsia/11966
https://ci.chromium.org/buildbot/chromium.fyi/Fuchsia/11885

which failed these two:
- AliveCheckerTest.NotifyThenStop
- PipelineIntegrationTest.ReinitRenderersWhileVideoTrackIsDisabled

I think wez already disabled the AliveCheckerTest, I'm not sure about the other one. If it's fixed or disabled then it's probably ok to put on the trybot.

I see.
FWIW I fixed PipelineIntegrationTest.ReinitRenderersWhileVideoTrackIsDisabled last week, see https://chromium-review.googlesource.com/c/chromium/src/+/809507.
It also looks like Wez disabled flaky AliveCheckerTests.
Are there any other known flakes?