We're going through the same thing right now with one of our old guys, except he is only 2 1/2. You have a very lucky old lady rat to live to be 3 1/2! That's really amazing! I always felt just making it to a 3 year birthday would be some kind of blessing, like a human making it to their 100th. Our guy sounds similar to your girl. He's lost a lot of weight, and is weak, and has lost the use of his back legs. The vet thinks it may be a combination of organ failure and/or a pituitary tumor. We keep hoping he will pass on his own, but he's been hanging on for months and steadily getting worse. He's on 2 different pain meds now which seem to help him feel better, but we've decided now that he will be put to sleep at the beginning of next week since it seems like he's just wanting to hang on, but seems like he has such low quality of life right now..
Is it possible for you to get pain meds for her? Surgery at her health and age is probably out of the question. As long as she's eating and drinking, she should hopefully be mostly ok. If you get pain meds for her, you can at least know that she isn't suffering much. But it's a balance for quality of life I guess, which is a really hard decision for us to make. Is she still able to do the things that she loves? The things that made her happy or that you felt she lived for when she was younger? Maybe she loved cuddling with you, or running on a wheel, or sleeping in hammocks, or exploring during free-range time, or climbing on things? If she's not able to do the things she really loved, and if she seems more unhappy now, it might be the most merciful to have her put to sleep. But if you're hoping she will pass at home on her own, you can try getting her some pain meds from the vet and at least make her more comfortable until her time comes. Try spoiling her and giving her high protein treats like a good quality wet cat food, or nutrient dense things like nutrical which most rats love. It's always good to encourage foods to seniors since they seem to lose their appetite easier. But loss of appetite is also a sign of pain, so try to maybe take notes on her to track her health maybe?
I know what you're going through, it's a tough situation. I hope she's able to pass away painlessly at home.