Mac internal/boot HD - "the disk you inserted is not readable by this computer"

My iMac has been playing up and I thought it was the system, but then it froze completely and I had to force quit. When I restarted it booted in to an external drive that has its own system, but my main HD won't mount with the message "the disk you inserted is not readable by this computer". Ouch.

Considering it will still spin (I've removed it and put it on a SATA USB connector) what software options are recommended for recovery and what should I expect? There are a lot of options out there but any recommended that aren't too expensive? Do they just recover fragments or a mess of files? Its a Seagate SATA drive 3TB I installed in 2016.

I've used Data Rescue before: https://www.prosofteng.com

You'll get a big load of files, without hierarchy or filenames.

Note for the future: you can buy a backup disk for less than most data recovery software costs.