Will publishing in a predatory-looking journal (because I’m being forced to) hurt my PhD prospects?

Hi everyone,
I’m currently pursuing my master’s degree, and one of our course requirements is to publish a research paper. Unfortunately, our professor is insisting that we submit it to a journal that looks extremely predatory — no impact factor, unclear peer review process, sketchy website, and overall bad vibes.

I’ve tried pushing back, but it seems I have no real choice if I want to pass the course. I haven’t published any papers before, so this would technically be my first publication.

My main concern is:
Will having this kind of publication on my record hurt my chances if I apply for a PhD at a more reputable institution later on? I do not plan to include it in my resume. I’m more so paranoid if somehow someone sees my name on that journal.

Any advice or insights would be really appreciated. Thanks.