Apple Account password not accepted in Settings on Mac Pro and iPhone

Thank you for answering. I was signed in on iCloud and either that allowed me to sign in here or I was able to sign in here because it is associated with iCloud, just not Settings. I cannot remember which but I am not signed into iCloud now so I definitely had to sign in here and I am making the assumption that this website is somehow associated with iCloud since my password is accepted.

Important: under "Sign in Security" where it says "change password" I thought it meant Apple password which I have been trying to change until iCloud accepted it. (This happened after spending an hour+ on Tracphone with Apple support who could not help me even though the verification was nnot sent to phone, blocked me before. and said go to Apple store, talked with helper then someone above her, mabe supervisor. but I figured it out next night, don't know how except I kept trying different things and typed in some alternative answers and Voila' MacAir accepted my apple id without asking to send text to phone to verify. Maybe somehow it learned I was locked out? So tonite I was typing my apple password again to change it and thought to try my MacAir Password instead of Apple password and it worked. So sign in security is just for sign in to this Mac I guess and my only problem was iCloud would not accept password (now called apple ID instead of password I guess because of the confusion. but now is. But I still do not know houw to change Apple ID. I think this should be easy to figure out. In the meantime I ordered from Amazon an ethernet switch so I could have both laptops online at the same time. For some reason I feel like my WIFI could be the problem and have stayed off. YES THE DAY BEFORE I WAS LOCKED OUT OF IPHONE I HAD A MESSAGE THAT IT HAD TO BE ERASED AND NEW DATA TRANSFER FROM MY MAC. I have never heard of that either but I had just transferred the data from back-up on my laptop and I was busy so just did what it asked, not anticipating the lockout the next day. It was then about 2 weeks old, around Oct. 3 just before 17 came out. I bought the 16 macpro thinking it was discounted but no. I needed a phone because my 14 is missing (Have it on ERASE). So tonight I will connect my new Mac Pro to ethernet and find out if icloud will accept my password there as it is accepting it here. I f all works out I will go to the page of explanation of how you unlock your phone using your laptop. Since my apple id was not working, because verification was need by iPhone where I was locked outI could not get past that to help iPhone. I am feeling very relieved. I guess. I don't understand why iCloud was rejecting my passwrd, still rejecting with Apple Support even before asking for phone number to verify on locked iPhone. then started accepting out of the Blue without verification on iPhone. So I think Mac Pro will also? we'll see. Thank you very much, I have no one to discuss this with except Apple Support and they made me go through the same steps that I had done 100,000 times already that did not work. I kept saying that my passwords were taped next to my trackpad always and they matched the keychain password for Apple, but at that point I could no longer access my keychain. I wonder if someone gained access to my iphone could they have then gained access to my laptops? Maybe got scared and undid everything. I know it sounds crazy but I will not be buying any phones or laptops again at Best Buy. Not accusing anyone but I did a few searches about the possibility and am left to wonder.