If by โparentโ you mean the source repo from which you branched, then yes, the methods you link to update your fork with the latest changes from the โparentโ repo (for the selected branch) without changing the โparentโ repo.
In the general case, transfer requests (PR) should not arise from the plug and aim at the โparentโ repo, this can also be the opposite (as shown in the related articles). You can also write PR from one branch to another branch within the same repo.
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