How to guide/teach toddler how to play with others?

Took my one year old to the library today. Up until now she hasn’t been around other babies or toddlers because she was really fussy as a newborn and as soon as her temperament became good to go out it was cold and flu season so I avoided other kids. Now she is sooo interested in other kids anywhere we go she stares in awe. I was actually so proud and impressed at her behavior at the library. She was bringing toys to every baby almost like a peace offering it was so sweet and walking up to other parents with the cheesiest smile.

So for the most part she did amazing, but there was a few times she’d walk up to other kids playing together and try to get in there and they didn’t seem interested in her joining, or she’d go up to another baby playing independently and try to take the toy. Obviously I went after her and would say “he was playing with that baby let’s go find another toy” but she doesn’t really understand anything yet so I almost feel silly saying that to her? Idk also some moms I could tell welcomed my baby walking up to theirs and some I felt like didn’t want mine near theirs. It was a new thing for both my baby and me. We had a blast and I want to keep taking her but it was different feeling so…idk - not confident? as a mom and how to handle her whereas at home I feel extremely confident with everything.

Just wondering if anyone has any tips for navigating play and manners and such in public - FTM with minor social anxiety overthinking 🥲