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GH-40954: [CI] Fix use of obsolete docker-compose command on Github Actions (#40949)

### Rationale for this change

The `docker-compose` utility is progressively being removed from GHA-provided runners:
https://github.com/actions/runner-images/issues/9557

### What changes are included in this PR?

Use `docker` client CLI directly instead of `docker-compose` where possible.

### Are these changes tested?

Yes, this should fix the sporadic CI failures because of the above migration.

### Are there any user-facing changes?

No, except additional optional env var `ARCHERY_DEBUG`.
* GitHub Issue: #40954

Authored-by: Antoine Pitrou <antoine@python.org>
Signed-off-by: Antoine Pitrou <antoine@python.org>