Change ID and register old ID

After this I will make a new Apple-id for private use with the username of the original ID.

Is this really possible? The original username is very important for me, I've used it for job applications and can't afford to lose it.

Apple does not have a statement about email address re-use in its documentation that I can find but here is an April 2021 post by ASC contributor IdrisSeabright that was recommended by the official Apple team -

"Once you've used an email address as an Apple ID, it can't be used again for an Apple ID, even if the first Apple ID has been deleted."

https://discussions.apple.com/thread/252629414?answerId=255095641022#255095641022

This is in accordance with what is claimed in this April 2021 post https://discussions.apple.com/thread/252629414

- Original post: "I tried contacting chat support and finally phone support today and they told me that you can NEVER use an email address that was used for a deleted account."

In other words, I don't think you can do what you wish to do. If you change the email address used for the old work account, it will not then be available for re-use with a new Apple ID.

Yes, it is. To get a new work ID, you need to create a new ID.

Apple ID - create a new.      

Apple ID – Create         

Family Sharing.         

Family Sharing - Set up.        

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. Also set up Family Sharing between the IDs to keep access to your apps/purchases. 

How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.        

What to do after you change your Apple ID or password - Apple Support.     

I may have misunderstood what you wanted to do. I was suggesting you create a new Apple ID for work using the links I posted above. Keep the current ID as is and start using it as your private Apple ID. By leaving the current ID as is, you retain the purchases and data from work.

You're welcome.