The right way to do this is to first claim your domain, then federate it, and then setup sync so everything works without you needing to do work. However, there are concerns and you should be aware of the limitations of Managed Apple IDs (MAIDs). Since it sounds like you've already created IDs using your domain, you will have more work to do.
Start with Apple's documentation on Federation.
On that page, there are links to setting up sync for Entra (Microsoft), G Suite (Google), and 3rd party identity providers. Choose the link that matches your identity provider and follow the steps to setup automatic sync of your users. This will allow the MAIDs to pass authentication to your identity provider, avoiding the creation of multiple passwords.
This all sounds great, but there is a catch. See here and understand the process of reclaiming the IDs. Users will receive an email asking them to migrate the ID. If the personal ID has purchases associated, they will stay with the user when they migration the ID to a new address. This will free up the original ID (using your company domain) so it can be used as a Managed Apple ID.
Next, make sure you understand the limitations of MAIDs. See here and read the bottom especially. A MAID cannot participate in any of the stores since it cannot have payment information associated to it. Thus, they also cannot be used for in-app purchases.
Hope this is helpful.