Hello Tom Geldner,
The missing PC under Microsoft account > Devices and the BitLocker recovery-key backup are separate issues. I would secure the recovery key first.
- Search for Manage BitLocker from Start and open it.
- Next to the Windows drive, select Back up your recovery key.
- Save it to your Microsoft account, a USB drive, a file on another device, or print it. Do not keep the only copy on the encrypted PC.
- Check your Microsoft account recovery-key page and confirm that the key is listed.
Microsoft cannot retrieve or recreate the key if it is lost, so I would complete this before troubleshooting why the desktop is absent from the Devices page.
The dsregcmd results do not by themselves indicate a problem here. They mainly show that this personal PC is not joined to a work or school organization.