I am trying BitBucket. I created a repo for testing, and then I am able to pull and push it successfully.
Then I made a fork and trying to push but SourceTree does not allow me to access the fork.

First, I'm logging in into BitBucket via Google account. Therefore I have no password for BitBucket.

OAuth is setting up.

It has two app passwords. I gave full permission for them.

I am able to pull and push the code. Then I created a fork on BitBucket, and added remote in the local repo to the fork.

Now I'm going to push it to the fork.

Then it asks me a password. I'm confusing because I have logged in to BitBucket via Google account, and it has no option to login from Google Account.

I used the app password, then I get this error.
I also tried "Forgot your password", but I don't receive any emails.

The fork is not set to 'private'.
How to access the forked repository?