I need to get the Apple password for my mini Mac. I forgot it and I purchased a new computer and need to transfer my documents

Are you looking for your login user name to your Mac mini?

Your Mac user account is your login user name to your Mac mini.

See the following Apple articles:

If you forgot your Mac login password -> https://support.apple.com/en-us/HT202860

Change the login password on Mac -> https://support.apple.com/en-gb/guide/mac-help/mchlp1550/mac

Reset your Mac login password -> https://support.apple.com/en-mn/guide/mac-help/mh35902/mac

If you can't reset your Mac login password -> https://support.apple.com/en-gb/HT212190

See also -> Ways to remember passwords on Mac

Ways to remember passwords on Mac – Apple Support (UK)

-----

BTW:

You are sign in here .  .  .  with your Apple ID & Password.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

What happens when you use the same Apple ID & Password that you use to sign in here?

See -> Sign in with your Apple ID -> Sign in with your Apple ID - Apple Support