How to recover files existed prior to formatting and reinstalling OSX on an internal hard drive?

Hi

I recently formatted the internal hard drive och my MacBook Pro Retina 13-inch, Early 2015 (Samsung SSD 970 EVO Plus 500 GB) and reinstalled a fresh copy of macOSX Monterey 12.3.1. The MacBook had the same OSX before formatting.

Now I need to recover some very important files which existed prior to formatting on the internal hard drive.

When I use an external drive as the startup disk and run utilities such as Disk Drill, they can only find files after reinstalling of the OSX.

Should I remove the internal SSD, put it in an external box and run the same utilities from a different Mac? Does it help?

Or there is a more appropriate recovering application or method which I can apply without needing to remove the internal drive?

Thank you in advance! 

/Abedi