My paper is posted to arXiv; how do I get it endorsed?
I think you have misunderstood how the endorsement system works.  Endorsement isn't something that's applied to an article, it's applied to an author.  It's a one-time process that some people have to go through in order to gain the privilege to submit articles.  Others are granted "automatic endorsement", by virtue of, say, having an academic email address

So if you have already been able to successfully submit a paper, then you don't need endorsement and you never will, and you should just ignore the whole thing.

If you had needed endorsement, you would not have been allowed to submit your first paper, and would instead have been given instructions that included the alphanumeric code.  You would then have given this code to your supervisor, and by logging into their arXiv account, they would have been able to use it to endorse you.  Then you would have been able to go ahead with submitting your paper.

The fact that you are not an endorser simply means that if someone else wants to submit their first paper and needs endorsement, you won't be able to be the one to endorse them.  You'll gain this privilege after you have more papers.  But you can't speed it up by being endorsed by someone else.