Watch issues
Why does my watch keep asking for the password for my husband’s Apple ID when I am signed into it with mine?
Apple Watch Series 5, watchOS 7
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A request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. After deleting the apps, it may be necessary to restart the device/computer before you can download the apps again. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID.
Or you can try to set up Family Sharing between the IDs to keep access to your purchases.