[Task]: Start services earlier in CI to be faster

[diox]

Description

#16061 introduced a new GitHub action to run tests in that doesn't spin up a full development environment.

Each job is waiting for MySQL to be healthy through depends_on, not as a separate step, so we don't see how long that takes. That may be an area to look into.

On top of that there is another 30 seconds to 1 minute to gain by being more clever with starting autograph: at the moment we are starting it for each job, separately, waiting for it to be healthy, which takes ~25 seconds. Given very few tests need autograph, we should look into marking them and running them in their own dedicated job, and stop starting autograph everywhere else.

Acceptance Criteria

• item 1

┆Issue is synchronized with this Jira Task

[diox]

On top of that there is another 30 seconds to 1 minute to gain by being more clever with starting autograph: at the moment we are starting it for each job, separately, waiting for it to be healthy, which takes ~25 seconds. Given very few tests need autograph, we should look into marking them and running them in their own dedicated job, and stop starting autograph everywhere else.

Note: test_search does have this kind of logic already. It's also explicitly waiting for Elasticsearch, which may be something we could look into - maybe we could remove the --wait, docker compose up -d elasticsearch, do other things, then docker compose up -d --wait elasticsearch before actually running the tests ?