Is my coworker being left out or is this justified?

I recently moved to a new town and started a new job in a department of 6 people. The other position that does the same job as me (let’s call her Jane) went on medical leave a few days after I started there. Before Jane came back, everyone in the department warned me I would adore her personally but dislike her professionally.

Jane is constantly procrastinating, making errors, and just generally being a nuisance. She will talk to me at my desk and be very clearly reading whatever I have on my screens, or will pick something up from my desk and read it without asking. All have happened multiple times.

Our other coworkers and manager have recruited me to help with stuff in the department or events at our company. Some of these are development activities that will help progress my career. Jane has made multiple comments to me that no one asks her to do stuff like they do me. The other coworkers said before I came to the company, she did not want to participate in all these extra things and they don’t understand why she is making a big deal of it now.

I am starting to feel bad and feel that she is being left out. Most things she is excluded from at work are things I am specifically being asked to participate in or volunteer for. I do not think she is being asked because she is difficult to work with. I have to deal with the negative comments if I’m asked to do something or volunteer to do something and she is not included.

Advice needed: Do I need to start declining these opportunities so she doesn’t feel left out? If not, how can I make it not so uncomfortable when she makes a negative comment? Because we are in the same position and split work, she is someone I have to interact with multiple times a day.