How to access files on old iMac retrieved HDD?

Well, those are not Time Machine files. It looks like the shop ran some forensic recovery tools on the disk and dumped things like the physical disks allocation table data and catalog data as text files (but without any file suffix so your computer is interpreting them incorrectly as Unix executable files).

If there are any useable files recovered, they should be under Macintosh HD. Or possibly "Lost Files", depending on how blunt-force the forensic recovery was.

I wouldn't expect too much - especially if the old Mac died of a disk failure. The fact that there is nothing on-screen under Macintosh HD after Extents Overflow is not a good sign.

In any case, the only things you could usefully get off a 14 year old machine are personal documents and the like. None of the old applications are going to work (except in the rarest of lucky circumstances) and there will be no dragging and dropping of any applications.

If you got the apps from the App Store, you will be able to download the newest versions using the same Apple ID. If you got them from Microsoft but had an Office 365 subscription, you can probably get it from Microsoft and log in to your account in the App.

Seems like the person who did this data recovery was most likely using Windows which is fine, but they were scanning the raw drive trying to pick stuff off instead of trying to clone the drive. Perhaps that was the only way to go, but the way I've seen some others do it & the way I used to do it (I am not a professional, but an advanced amateur) was to scan the raw data in sequence to pull the raw data to another physical drive or a raw image file so that I could work on trying to access the actual files while working from a good drive. This person seems to have tried to recover files directly from the failing hard drive which is not a good way to go in my opinion. For recovering a Windows drive, their approach may work out better than it has here, but for macOS it does not work well.

If your files are not in the "Lost Files" folder, then they were unsuccessful at recovering any data. Your data most likely will no longer have their original file/folder names since file/folder names cannot be recovered when using their method...you will need to use the file types to try to figure out which files may contain your data....it won't be easy since the drive will be full of temp & cache files that will look a lot like the data you are trying to recover.

You usually only get one chance at recovering data from a failing hard drive since that one attempt will usually degrade the health of the hard drive beyond any hope of making a second attempt.

As stated in the reply above, that looks like a disk dump, showing the contents of the various partitions.

Not Time Machine.

Those are partitions and files related to booting the Mac.

That’s not showing any user data.

If the failed iMac was using a Fusion drive, it’s conceivable that’s a dump of the contents of the SSD, and the HDD was not dumped, or was bricked.

Depending on the vintage of macOS, the user data would be in Macintosh HD or Macintosh HD Data partition. If that partition and that data is present.