New iPhone 13 does not receive some texts, but they go to my old iphone

Ok so this is a peculiar problem:

I got a new IPhone with a new phone number recently. It is all fine except when a contact who had my contact before texts my new number, it does not go to my new iPhone but goes to the old one. This is can kind of be solved by me texting that person first from my new phone, and then I can get messages from them. However it is annoying because I have no way of knowing if this happened and people think I am ignoring them lol, unless I check the old phone regularly.

this doesn’t seem to be a problem with people who are texting me for the first time, or who don’t have an iphone themselves.

I even tried to turn off iMessage and FaceTime on the old phone but that didn’t help. Then I would never see the messages people would try to send, so I turned it back on for now so I could check if anything came.

lmk if you have any ideas on how to fix!