Well, I don't know your girlfriend and cant say if she is over obsessed with her grandmother ))) But frankly, I would say that this will be rather normal behavior for a girl who was raised by her grandparents. Don't stress (!), it doesn't mean that she didn't grow up. Maybe like many children who were born in Soviet (or post-Soviet) country she just probably never had a nanny and was raised by her grandmother.
To have an extra help in raising kids in Soviet culture was considered "bourgeois" and highly suspicious. People had neither money nor services available. So since almost all mothers had to return to work when the child was 1-3 years old, the kids had to be put in the nursery or left with someone from the family.
This special someone was often a grandmother. Quite often a grandmother-to-be would retire when her first grandchild is born...And she will begin a new full-time job with no term of retirement )))))
It will be grandmother who will be replacing mother/nanny/siblings for many kids.
She will be the one who will spoil, teach, congratulate the first!
....This of cause can (and often does) cause a serious tension between a mother and a grandmother . Who one wants to share a love of a child? )))
Still if you want to know how people of ex-USSR feel about their babushka. Ask them who was their babushka...and you will a right to see a tear in their eyes, smile and a long story of the best kotletki (meatballs) ever!!!!
P.S. So don't be surprised, if your Russian mother-in-law will be against hiring a nanny when you have a baby and will be ready to take full care of YOUR child ))). She knows that her effort will be fully paid back.
She will be loved by her grandchildren and......they will be cuddly until a very mature age )))....and will memorize every moment spent together (on the datcha, for example)