Optimize execution duration of Sync Github Organization Settings Action

We have 210 archived repositories and it looks like the automation needs 12 seconds to check on a single archived repository. Logs:

{"client":"github","component":"peribolos","level":"info","msg":"GetRepo(cloudfoundry, stembuild)","severity":"info","time":"2025-06-10T01:52:06Z"}
{"component":"peribolos","level":"info","msg":"repo \"stembuild\" is archived, skipping changes","repo":"stembuild","severity":"info","time":"2025-06-10T01:52:18Z"}

....

{"client":"github","component":"peribolos","level":"info","msg":"GetRepo(cloudfoundry, stembuild)","severity":"info","time":"2025-06-09T12:38:32Z"}
{"component":"peribolos","level":"info","msg":"repo \"stembuild\" is archived, skipping changes","repo":"stembuild","severity":"info","time":"2025-06-09T12:38:44Z"}

....

{"client":"github","component":"peribolos","level":"info","msg":"GetRepo(cloudfoundry, route-registrar)","severity":"info","time":"2025-06-09T13:27:20Z"}
{"component":"peribolos","level":"info","msg":"repo \"route-registrar\" is archived, skipping changes","repo":"route-registrar","severity":"info","time":"2025-06-09T13:27:32Z"}

That means we could save 210 × 12 = 2520 / 60 = 42 min on each run of the Sync Github Organization Settings which needs currently more than 7 hours per ran.

Start with the linked Sync Github Organization Settings workflow and trace the archived-repository check shown in the logs. Determine why each archived repository takes about 12 seconds, then verify that archived repositories are skipped more efficiently and that the workflow runtime is substantially reduced from more than seven hours.