Coworker is making me uncomfortable

I [F28] work at a fairly large corporate company in a huge department. Just for some background, in that department we're split into teams between 15-30 people and we sometimes will never interact with other teams. The role is hybrid so we have designated days during the week that we're required in office but majority are working from home.

I started at the company fresh out of college 5 years ago. I was hired with a pretty large group mixed with other recent grads, and internal people that were transitioning to my department. We would have Zoom meetings almost daily for training, getting to know each other etc.

During a few of these meetings, I had to speak. Introducing myself, asking questions etc and almost every time I did that this guy lets call Jim, that was not assigned to my team (but in the same department), would message me privately on Teams. He would make comments about my background (which was my bedroom of my apartment), ask me personal questions about myself and about where I lived. It gave me bad vibes so I just stopped responding to him since I was also trying to work.

Also this guy is easily in his late 40s, I was about 23 when I got hired.

Moving forward, Jim left me alone and didn't push it after I stopped responding. After the pandemic we were required to go back into the office a few days a week and I would see him and avoid him based on a gut feeling.

Since then he will occasionally try to talk to me, sit near me, and stare at me constantly. The way our office works is it's basically 5 floors of cubicles. Each department gets assigned to a zone/floor and you're required to sit with your 15-30 person team, but other teams are able to sit nearby. He's on another team but will move where he sits based on where I'm sitting (we do not have assigned seats within these zones, just that we should be grouped with our team).

One time a few months ago he came up to my desk out of nowhere standing really close making a joke about something on my screen and was trying to touch my arm and shoulder while laughing. I'm telling you that when this guy comes near me I am immediately afraid and on the defense which doesn't happen to me often. I consider myself pretty friendly and outgoing when I have to be. I shifted away from every unwanted touch that he was attempting.

Yesterday a coworker on my team came over me and told me her old manager (that she's close with) came up to her to ask if she knew whether I was single or in a relationship. Coworker asked why he was wondering, and manager said "Jim has no game and asked me to ask around." When my coworker told me that, my heart dropped and I felt immediately anxious.

Not that it should matter, but I am in a long term relationship and live with my boyfriend. Coworker told her manager that, who I'm guessing will relay it to Jim next time we're in office.

Here's my dilemma: I feel uncomfortable that a MANAGER even followed through with that request (we literally have sexual harassment/what's not okay in an office trainings constantly) to ask someone else on my team about my relationship status.

Jim makes my skin crawl when I make eye contact with him and feel even worse when he tries to sit near me.

However, he hasn't tried anything or been forward with me at all. Still, my close friends, boyfriend and mom suggested I file a report with HR for Jim in general and the manager for being unprofessional.

So yes he's making me uncomfortable and he gives me a bad feeling but is that enough to report what happened? I don't want to make a big deal out of something small but at the same time I was honestly raised to be hyper-aware of my own safety around men.

I'm worried the answer that I'm not single won't stop his behavior, but I also feel like maybe I should give it a chance to see if it will. But also at the same time, I don't think what the manager did was ok.

What do I do?