dispatcher: docker test shell: ensure stage is set properly

It turns out the job parser only assigns the correct stage parameters to
tests that declare that they need an overlay. In the case where docker
and target tests are mixed in the same job, this will cause the tests
intended for docker to also end up in the target, but this is probably
not a big deal since they won't be executed anyway.
15 jobs for more-docker-fixes in 15 minutes and 50 seconds (queued for 3 seconds)
Status Job ID Name Coverage
  Test
passed #94383
amd64
dispatcher-debian-10

00:02:22

passed #94385
amd64
dispatcher-debian-11

00:02:21

passed #94384
amd64
server-debian-10

00:02:51

passed #94386
amd64
server-debian-11

00:05:04

 
  Analyze
passed #94388
amd64
black

00:00:33

passed #94389
amd64
code_quality

00:00:21

passed #94390
amd64
coverage

00:06:27

59.3%
passed #94391
amd64
dockerfiles

00:00:19

passed #94393
amd64
pylint

00:03:00

passed #94387
amd64-dind
sast

00:02:17

passed #94392
amd64
schemas

00:00:31

 
  Build
passed #94395
amd64
debian/10

00:01:24

passed #94394
amd64
doc

00:00:40

passed #94396
amd64-dind
docker-amd64-dispatcher

00:03:39

passed #94397
amd64-dind
docker-amd64-server

00:04:14