My girl cat, Crystal, is like that. She will go off on her own for a few minutes at a time here and there, but she is basically my shadow. Apparently it is unsafe for me to go in the bathroom alone. I might get a crazy notion to step into that little water-pouring room and get all wet, in which case she MUST hold me still and dry my feet. I keep doing it -- I can't seem to learn how ridiculous it is to keep getting in there when every time water pours out from overhead.
She also stands up and meows about a dozen times a day to be picked up and cuddled. If I sit down to dinner, she sits politely on the bench next to me. Mealtimes are a time to sit at the table, you know. She never begs (well, unless maybe if tuna or turkey is involved, then she will press her head against my arm and look lovingly at me. She is always by me or on me if I am on the bed or couch. If I spread a newspaper or book, she recognizes that I am making a special place for her to climb onto so I can pet her. She is highly honored to be sleeping in the bedroom instead of the catroom. And I'm starting to realize how fortunate I am that she sleeps at the FOOT of my bed, only approaching me purring for attention when I wake up, change position, or otherwise indicate that I want her to come.
The only way I can be in a room by myself is to go to a door like I am going to go through it, and she stands up to help me open it. If I open it, she will run through, then I close it. It takes about two minutes before she gets upset and starts mewing to be let back in.
Fortunately she respects me being on the laptop, but not so posting from my phone, which is why typing this message has taken recover 30 minutes now LOL. (And I'm fairly fast typing on this little screen)
Enjoy your lovey kitty. Most of mine have been satisfied with one or a few brief love-sessions a day and go their own way otherwise. But an attached cat is not unheard-of.