FWIW, I agree with you that # of papers is not going to matter to some hiring managers. Are you strong at coding? When I've hired research engineers, the most important things I've looked for are performance in a take-home coding challenge, and their technical creativity in approaching daunting problems.
I once attended an hackaton, and a guy doing a Phd in ML joined our team.
It turned out he was completely unable to figure out how to run a python application with 2 dependencies on his machine.
He also didn't understand the HTTP protocol and kept insisting that for the users of our website to send us a request with some payload, they needed to sftp a file with the request, and then click on the website to process their file.
I kept telling him that since the server was mine, I wasn't going to open up ssh access to the world and a POST request had to do.
Of course he didn't know what a POST request is, and kept insisting on a loop that I had to enable sftp to upload files.
Ended up with me shouting, him doing absolutely nothing besides wasting time, and everybody seeing me as the bad guy for shouting.
In the end I stuck around long enough to deliver something and present it, and left immediately after; not staying to see if we had won something.
That was the last time I attended an hackaton.
As a result, I think when hiring I would be very very careful to select someone with a Phd in ML, as they might have done no programming whatsoever in their whole life.
For some extra context, I have been applying every ML research engineer/scientist job that would take a new grad.
I don't have any sense for what a hiring manager wants, it's especially hard with all the layoffs, I'm sure plenty of people are applying for the same research engineer positions. I certainly consider myself to be strong at coding. I've done a couple coding challenges on hackerrank that I do well on. But I have not been lucky at getting a phone interview yet. (I do have a personal website and CV)
Sounds like you need to network more, get the lay of the land of what’s being expected. Remind yourself that while you’re not at the vanguard you’re still cream of the crop; phd tends to sap out social skills and hence for many of us finding the first job is the most daunting thing possibly in all our lives. Slog through and after that it’ll be fun sailing for the most part.
Do you have a personal website with a C.V.?