Relationships with godparents are quite varied, depending on the family.
My godparents were10 & 12 when I was baptized. They were my cousins and we really didn’t have more than a cousin relationship.
My children’s godparents hardly ever see them. In fact, the youngest hasn’t seen his godmother (my cousin) or probably heard from her since he was 4 and we moved clear across the country. His godfather, or rather Christian witness although that was never explained to us, his dad’s brother also lives far away and stays away from the family as much as he can.
I’m godmother to 3. One is my godmother’s daughter and she’s in her 40s. We have a great relationship but it’s not godmother/goddaughter because I was only 16 when she was born and wasn’t really allowed to be a godmother beyond the Christmas & birthday gifts and presence at her Confirmation.
The next is the child of friends who split up when she and her twin were 2. Mother has custody and is a non-Catholic, total non-believer. Dad never did his Catholic duty beyond having them baptized to please his mother. We were picked because we were friends and they knew I was Catholic and they were told they had to have a Catholic at the ceremony that didn’t mean much to either of them. They had no expectations that we’d be involved beyond the ceremony.
The girls will soon be 13 and have no Catholic instruction. We never felt we could talk to either one about this because the situation is too delicate. From a situation where we used to have family dinners together regularly we’ve gone to awkward ‘hellos’ as we meet him and the woman he left his wife for. The mother and the children have moved away and we only see them if we happen to be in that city, something that might happen once a year or less.
By contrast, the latest is 6 months and Church is important to the young family. We will be allowed to be involved in her religious life as she grows, in fact we were chosen because, to quote the mom, “You’re the one I’d send her to if she has any questions about the faith.” Although we are not related, we have become “aunt & uncle” to all the children in that family over the last 8 years so had a family relationship before being asked to be godmother/Christian witness. They picked us for the right reason and not simply because they didn’t know anyone else.