Hello azhomebpo,
We would like to see how we can help you with signing out of iCloud with your Apple ID. You will need to delete any apps downloaded under your old Apple ID, and download through your new Apple ID. You will be prompted for the old Apple ID for any updates until you have downloaded under your new ID. Follow the steps in this link to sign out of iCloud: Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support
"Sign out on your Mac
In macOS Ventura or later:
- Choose Apple menu > System Settings.
- Click your name.

3.Click Sign Out.
4.If you want to a keep a copy of your iCloud data on your Mac before you sign out, make sure that you select the appropriate checkboxes. Then click Keep a Copy.
5.If you want to keep a copy of your Safari passwords on your Mac, click Keep on This Mac.
In macOS Monterey or earlier:
- Choose Apple menu > System Preferences.
- Click Apple ID, then click Overview.
- Click Sign Out.
- If you want to a keep a copy of your iCloud data on your Mac before you sign out, make sure that you select the appropriate checkboxes. Then click Keep a Copy.
- If you want to keep a copy of your Safari passwords on your Mac, click Keep on This Mac."
Cheers!