Neighbors' occasionally outdoor cat has made us her go-to people

Our downstairs neighbor has a kitty that's been outdoors more frequently this past year than in years prior. The cat is like 10, and so lovely. We are a pet-free household, but my spouse and child love how sweet and lovey this kitty is, so they always give pets and scratches when we see her outside.

In the past few months, this cat has been found on our porch in front of our door, mewing as soon as we open it to leave in the morning, mewing at the screen in the evenings, and even following us up the stairs when we come home from places. Sometimes she follows us inside when we can't get the door closed behind us quickly enough (like if hands are full or child is coming inside). We have given her water frequently when it seems like she's been outside for a bit, or it's particularly warm/cold, and even have given her some food a couple times.

It's become uncomfortable, since this cat literally lives below us. I know the mom is on disability for chronic pain management issues, which also comes with occasional med changes, and the dad is usually dealing with that or work, and their tween daughter probably mostly deals with the cat, but sometimes is at her other parents house and not around.

I don't want to cause a rift with the neighbor by going to management. We have a few outside kitties, all of which are lovely, and we'd hate to have that taken away from the cats who enjoy being outside sometimes. Would it be ok to write a friendly note to the neighbor in this instance? Like "hey, we aren't trying to take your cat but she seems to need more than she's getting, can we help out?" kind of thing?

We are cordial with them, but only chat upon infrequent passing by, and don't have each other's numbers