How to switch user Apple ids on Apple HomePod

You can set up Multiple Users but you can only have one primary user. You would have to reset it, then set it up again on another Apple ID to switch the Primary user account

HomePod mini and HomePod support up to six users in a home

Set up voice recognition on HomePod mini or HomePod - Apple Support

You don't need voice recognition to change to another AppleID, if all you are seeking is the use Apple Music associated with an AppleID on the Homepod. Just change the Primary User for the Homepod settings in the Home app on an iPhone or iPad.