dev: Trim back the overgrown CI jobs

[victorlin]

Same reasoning as @tsibley in nextstrain/cli@fab709a:

Running on push and PRs is often redundant. For PRs, we really care
about the putative merge of the PR branch, and that's what "on:
pull_request" tests. We typically do not need push-level CI results for
PRs. On the other hand, CI results for every push to master are nice to
have both as a safety backstop and for the linear chain of CI history it
produces (e.g. to debug the impact of external changes on our CI).

The primary downside I see is that you can no longer push without
opening a PR just to see what CI says, but I think that's an acceptable
tradeoff, especially now that draft PRs are a thing. To mitigate this
downside, "on: workflow_dispatch" allows CI to be manually dispatched
for a specific branch/tag/commit if you really don't want to open even
a draft PR.

Trimming unnecessary CI jobs reduces the time to completion for CI runs
(good for the dev loop) and reduces organization-level job queuing,
which can negatively impact the workflows of other repos.

Noting that another downside is not having push-triggered CI runs on forks, but workflow_dispatch and draft PRs are good alternatives.