Small clean up of the fleet gateway "run" function implementation

[aleksmaus]

What does this PR do?

Small clean up of the fleet gateway "run" function implementation

Why is it important?

Just stumbled upon this piece and I think it can be simplified, one less go routine.

Checklist

• My code follows the style guidelines of this project

How to test this PR locally

Regression test with the fleet

[mergify]

This pull request does not have a backport label. Could you fix it @aleksmaus? 🙏
To fixup this pull request, you need to add the backport labels for the needed
branches, such as:

• backport-v./d./d./d is the label to automatically backport to the 8./d branch. /d is the digit

NOTE: backport-skip has been added to this pull request.

[elasticmachine]

Pinging @elastic/elastic-agent-control-plane (Team:Elastic-Agent-Control-Plane)

[aleksmaus]

docker: Error response from daemon: Head "https://docker.elastic.co/v2/beats-dev/fpm/manifests/1.13.1": Get "https://docker-auth.elastic.co/auth?account=jenkins_ro&scope=repository%3Abeats-dev%2Ffpm%3Apull&service=token-service": net/http: request canceled while waiting for connection (Client.Timeout exceeded while awaiting headers).

sigh

[elastic-sonarqube]

Quality Gate passed

Issues
0 New issues
0 Fixed issues
0 Accepted issues

Measures
0 Security Hotspots
100.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube