You make friends by being honest and interested in others.
Not deep honest at first but by indicating publicly that you are not perfect.
Accept not everyone will like you. And that's ok.
Thank people at the school gates even if they are giving you information you already know. "You can't put peanut butter sandwiches in the packed lunch for the school trip". "Oh I wasn't going to just in case but thanks for the reminder appreciated" not "yes I already know that"
Don't come across as a know it all.
But also don't come across as a doormat
Be confident, humble, honest, thankful, join in, don't boast about your kids or compare.
It just takes time. And trial and error.
If someone gossips, oh her and her husband split up, try "well it's a shame to hear of any family breakup regardless of the circumstances" type thing. Don't judge especially on gossip it's rarely the whole truth.
Volunteer on the PTA. Yes there will be a bossy mum or two but there has to be to get stuff done. Remember they are giving time, their own money usually, petrol, favours, to help your children's school. Say thank you.
Step by step
Don't get offended.
Be kind.
Forgive people if they mess up from time to time.
Don't expect them to be how you think a person should be.
Relax, have fun, join in, enjoy joining in, if only for the company you have whilst doing it.
As for some saying, I can't give time to people, I don't want to listen to their problems, I can't be bothered with making friends, most people are toxic and just use you, well yes if you think that you won't have any friendships. Friendships do listen to EACH OTHER, I spent a whole unbroken half hour, more or less, ranting on the phone in the car at school pick up yesterday because I needed to, it was my turn, I obviously do the listening as well. But even in my ranting I was trying to make friend laugh and when I did let her get a word in she managed to squeeze in a paragraph of advise that was gold dust and I really needed so I feel better now. But that gold dust wouldn't have happened without the previous 15 minutes of solid whinging from my side. So I texted her later and said thanks that really helped me out. Because it has and I appreciate it.
What have you got to lose?