Many adults or kids of any age will happily let other people act as unpaid staff. Often it's because they have become used to this in the past, e.g. my DD's Uni accommodations contained some lazy people who never cleaned or empty bins, and used other people's stuff all the time. The worst were generally from rich families abroad who had staff, and had never cooked or cleaned in their life before, and just assumed someone else would do it.
So that's problem 1 - the routine problem of getting the GF to step up. There will be plenty of tactics on this online, it's a standard problem. If they were a couple without a child, this would be simpler and easier, but of course you will be wanting to avoid losing contact with your GC, so it makes it tricky. I don't claim to be an expert, and I'd say it might be worth getting professional advice, even if it's from a charity, since this is a high-stakes negotiation really, whereas there are plenty of posters on here who are happy to offer advice on any issues to be confrontational and risk burning bridges and connections for the future. Maybe even relationship counselling, I really don't know what's best.
Problem 2 is the money. I would always assume that most grown up kids in their 20s and 30s with a job, when not asked to pay rent or bills, will find something else to spend the money on, typically cars, entertainment, holidays, gadgets or holidays. This is a bad thing, especially if it's a long-term commitment like a car on finance. Try to avoid this happening. My plan was to charge rent and board, and save it for our kids for use as a house deposit.
We have DD at home, but our stinginess has rubbed off on her, and she hardly spends a penny, and is building up savings fast herself, but I think that's pretty unusual.
Problem 3 is housing:
assuming the relationship lasts, which needs a separate discussion really, what is available in your area?
Where I live, there are some shared-ownership options, including 2 bed flats in a nice town in the north-west for £25k for 25% ownership, and then a rent of £494.13 pcm this includes the 75% payment to the housing association and also includes the service charge and Ground Rent. Your area might be more or less expensive, but worth looking at this and affordable housing on your local council website