You are doing exactly the right thing op. As a mother to similar age teens and a child that got heavily involved in a relationship at 16.
Your dd probably thinks she is old enough for a serious relationship, and probably idolises her boyfriend, but you know better. It’s a 3 month relationship in reality (so barely out of the traps) and at 16 ( or any age) it doesn’t equate to a ‘serious long term’ relationship. It just doesn’t. It wouldn’t for me until she is 18 plus anyway, and we are talking years not weeks or months.
I would approach it carefully. Yes he seems to be a very nice boy but taking your time is essential in new relationships, try to encourage her not to drop her friends and hobbies and remind her she will need these things if it doesn’t work out.
He will not be staying at your house until well into adulthood full stop, but maybe compromise with her staying with him at the weekends so she doesn’t fall behind at school?
I would invite him for dinner, family bbqs and the odd outing and perhaps meet his parents too at a push this Christmas if they are still together.
Encouraging dd to get so emotionally enmeshed is really not healthy at all for her, and whilst acknowledging she is technically old enough for sex, it doesn’t get mean she is emotionally ready. She could quickly find herself out of her depth and she needs you as a solid, dependable anchor to help keep her boundaries in place even if she is unaware she needs them at all, and is being swept off her feet.
Be unfailingly polite and welcoming but distant. Do everything you can to ensure you spend time with her as a family. He may have charmed her but that does not give him the green light to access your home and private family life. DD needs to understand this is the preserve of a committed relationship of many many years, and in time you will gladly enjoy a deepening relationship with him and it will happen naturally as they get older etc.
Don’t be afraid to stick to your values op, she is still a child until she is eighteen and still needs you to parent and guide her fully. Perhaps now more than ever.