Is my manager acting inappropriately?

I really struggle interpreting human interactions so I need a bit of support here! Also, sorry if the formatting is weird, I posted this from my phone.

I (30F) have worked in my current position for almost a year now but with the same company for 4 years. My boss "Tom" (M55) is a really great, supportive boss and just seems to be a really nice guy all around. We work in a really difficult, emotionally draining field (CPS-adjacent) and since I got this position, I have felt really great going into work knowing I won't get thrown under the bus or be underappreciated like my last position.

Now that I've been in this job for a bit, I feel like my boss might be too nice to me... Maybe even flirtatious at times? I feel like some of my reading into these interactions is because I've never had an actually nice, supportive boss (in this field, at least) and I might be misinterpreting normal interactions?

All of these interactions are quite small but I don't know if they add up to anything... - If I have a plate or mug in my office at the end of the day, he will offer to wash it. I asked a coworker if Tom ever offers to wash her dishes, she said he never has. - Once, after a really difficult work phone call, I put my head in my hands on my desk. He walked past my office and he rubbed my upper back, like between my shoulder blades, for like 3 seconds. It felt like it was a bit inappropriate but honestly in that moment, I really needed that back rub... - I had bronchitis and my cough lingered for a while. After one of my coughing fits, he came into my office and offered me some cough candies. The next morning there was a pack of fisherman's friends on my desk. (This totally could have been a way to keep me quiet in the office though). - We banter like a lot. We are quite joke-y with each other (when appropriate). - Whenever I work late and outside of the office, he asks if I can text him (my work phone to his work phone) once I get back to the office. Again, I asked my coworker if he requests this from her and she said no so it's not protocol.

Thank you for reading and any and all interpretations! I appreciate your time!