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GH-36224: [CI] Update rest api invocations in GitHub scripts (#36225)

The rest api calls were moved into from `github.` to `github.rest.` so the workflows are failing after the update to gh script v6.

### Are these changes tested?

As these changes are in priviliged workflows testing is only possible after merge.

Closes #36224 

Authored-by: Jacob Wujciak-Jens <jacob@wujciak.de>
Signed-off-by: Sutou Kouhei <kou@clear-code.com>