It was hard to find a solution for this until I reworded my search phrase and found it in two forums out of many deep dives. References at the end of this post.
Changes made on Mozilla Thunderbird or in iCloud Contacts will synchronize across all locations. Some of the same details can be used to set up your iCloud Contacts account with Microsoft People on Windows 11 if you prefer to use Microsoft Mail and Calendar from the Microsoft Store.
These set of instructions were performed on macOS with Mozilla Thunderbird. Your experience may vary if you are on Windows 11.
1. Go to Address Book in Mozilla Thunderbird and add a new CardDAV address book.
2. Put your iCloud email address in Username and https://contacts.icloud.com/contacts/ in Location.
3. Sign in to your Apple Account (https://appleid.apple.com/sign-in) and under Sign-in and Security click on App-Specific Passwords block.
4. Generate your new App-Specific Password by clicking on the plus symbol to the right of the dialog and give a name to the purpose of the generated password that will be a reminder to you in the future. I recommend the name of the application you will use it for and the name of function within the application. Click on Create.
5. In the next dialog enter in your Apple Account’s password and click on Continue.
6. Now you should see your new generated App-Specific Password. Copy it exactly as you see it before selecting Done.
7. Back in Mozilla Thunderbird you should see this first dialog box. Put in the App-Specific Password. Then the second dialog box will appear with a different address and you will put in the same App-Specific Password.
8. Now you will see a dialog box with a “card” CardDAV address book from iCloud and click on Continue.
9. You are taken back to the list of address books with “card” in the list. Click on the horizontal three dots at the end and if this is your only address book then click on Default startup directory. Reopen the dropdown menu and click on Properties.
10. Change “card” to “iCloud Contacts” and “every 30 minutes” to “every 5 minutes” then click on OK.
11. If you make a change on your Apple devices and have iCloud enabled for Contacts then you should see the change after five minutes. If you want to see the change sooner, click on the horizontal three dots on iCloud Contacts and then click on Synchronize or set the Synchronize time from “every 5 minutes” to “every one minute” in Properties.