That said, the professor is a mandatory reporter under federal law. Either she is aware of violations and has reported them, or she doesn’t believe that what is happening crosses that line.
Especially when she writes that students have complained to her. If it even begins to sound like a Title IX violation, you interrupt to tell them that you are legally required to make a report of anything they tell you and offer to let them continue talking or that you will personally escort them to the university office where they can talk to someone that is not legally required to make a report. You absolutely do not solicit the internet for advice.
So this is dumb, creepy, and uncool. But it’s not a Title IX issue.
Only because the first options of reaching out to department members and administration went completely ignored. I certainly wouldn't file a formal complaint as my first action in this case (as described), but at a minimum the people who work there have experience dealing with situations like this, and could offer advice to the professor, or perhaps have a discussion with the administration about how to prevent this situation from escalating into a Title IX issue.
While I normally would argue about virtue signaling, this seems like creepy and unsettling behavior that definitely warrants an investigation. That doesn’t mean there was any rule breaking, but this is one of those creepy things that I strongly oppose looking the other way at. If you’re afraid of an investigation, then it is probably something worthwhile looking into.
