How do I inherit Time Machine backup from an old MacBook Pro on a new one?

Now there are two files on the backup drive, one for each computer.

"Files?" Should be a folder, either Timestamped (APFS format) or named for the Mac (older, HFS+ format). If they look like files and not folders, then is it a network backup? That is an important distinction that directly impacts your question.

They both work, 7 years of backup on the Intel Mac work fine on the old machine. New machine backing up normally, but won’t access old backups. Nothing erased, never a question about where anything should go.

If it is a network backup destination, then it will create a separate Sparse Bundle Disk Image for every computer.

If it is an APFS backup scheme on a direct-connected drive it must erase the drive to start over. There is only ever one APFS backup allowed on a volume.

If it is using the old HFS+ scheme, then it probably recognized that on the drive and created a new folder, but both should be inside a Backups.backup folder (doesn't sound like that).

Normally, all that's needed is to use Migration Assistant then connect the backup to the new Mac, and you are prompted to claim the backups on the drive.

"Your Mac might ask whether this computer should claim existing backups created on a different computer. Claim the backups if you want them to become part of the backups for this Mac."

Back up your Mac with Time Machine - Apple Support

https://eclecticlight.co/2024/11/12/migrating-to-a-new-mac-and-claiming-time-machine-backups/

Only if you erase the drive.

Do any destination disks show up in your TM settings pane (System Settings > General > Time Machine)? With the drive connected, try clicking the (+) at the bottom of the box and see if you receive the prompt.

If I just tell TM to backup the new Mac, will it erase the 7 years of backup on the drive?

If it doesn’t ask about inheriting the existing backup when you add it, then it will erase the drive if you continue.