Totally get you OP. I too was like this when I was younger. Introvert, but seemed to attract needy people and couldn't say no to them. Then once you've got sucked in and try to say no sometimes, you feel really mean. Whereas people who can just breeze along and not get targeted by these types don't have to feel mean at all.
It is all about boundaries, looking people in the eye and saying no, you don't want to, that doesn't work for you at the moment, you already have plans, etc. And yes, upsetting them. But you have to remember that they don't give two shits that they're making life really hard for you. Unlike you, this type of manipulative person is only thinking of themselves, and they can sniff out a people-pleaser from miles away. Yes, people need support and life is tough, but that doesn't mean you are obliged to put your own life second for anyone who decides to make demands on you.
I've had elderly neighbours who literally held onto my arm when I tried to leave a chat to get on with stuff. But I had to just find some ovaries and say "I'm sorry, lovely to chat but I'm off to work now." And walk away.
With your needy friend: "I can't make it this week." "Thank you for asking, but I'm not available at the moment." "No, I have plans." I know how it feels, you feel so pressured and awful, and it feels like kicking a puppy, but that is the situation these people set up. She cooks for you so that you'll feel awful saying no. I'm not saying she's evil and cunning, she's just doing what's always worked for her, but you don't have to engage with it.
I'm now much older, and my life is busy with kids and work, and I've learned to prioritise my alone time because it's so precious and I need it. Yes, it makes me a bit anti-social, I don't go out much or see friends as much as I should maybe, but for the time being my mental health and priorities have to come first.
I now find it so much easier after lots of practice. There's a local cafe I sometimes go to and there's a man who's always in there and always talks to everyone and looks for someone who'll let him chat to them. I now am able to say "Hi X, how are you", have a 2 minute chat, then say "I've come in here to read my magazine, that's what I'm going to do now, so see you later" . I'm sorry for him if he's lonely, but if I let him he'd follow me home. Boundaries.
Read this book too - it will really, really help I promise:
A woman in your Own Right