[CI] Link-check push step not working

[chalin]

See https://github.com/open-telemetry/opentelemetry.io/actions/runs/13075527624/job/36486655690?pr=6145.

[svrnm]

is this a one off issue or still ongoing?

[chalin]

Still ongoing. I commented out the push code in the meantime. I haven't gotten back to it yet.