Use self-hosted runners for republish workflow

[damccorm]

This is failing with likely the same problem as #33506 - switching to self-hosted to mitigate the problem

Example where this fixed the problem - https://github.com/apache/beam/actions/runs/12639184719
Very red history before this fix - https://github.com/apache/beam/actions/workflows/republish_released_docker_containers.yml

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[damccorm]

I verified this will work on my fork once our secrets are updated (published this artifact with this run before cancelling it).

Publishing PR to get feedback, but will wait on merging until secrets are added

[damccorm]

R: @claudevdm

[github-actions]

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[damccorm]

New secrets have been added - I will let this run complete before merging, but it looks like it is working so far - https://github.com/apache/beam/actions/runs/12709820895/job/35429609977