Hi!
Welcome to community!
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You did a storage and a CPU tests, but we still did not post your:
-) log excerpts of issue you got;
-) machine config.
Please check [HowTo] Provide System Information and also try [HowTo] Request support and post your research results: may be for someone it will be a hint to suggest something.
Also you did S.M.A.R.T. test, but may be it is current run-related test results, but not shows previous issues/failures during earlier usage. What about to check the report of sudo smartctl -x /dev/sdX in term of what looks bad there?
May be over(under- ?)heating issues?
If you can easily find other cables, try to change SATA data cable.
In case of non-cable setup, try to change port you use for your storage. Before to do it clean the port with vacuum cleaner to get rid of dust as maximum as you can.
Check BIOS modes of your storage and what modes are actually supported by the storage model.
Also, electrical contacts are vulnerable to high electrical current: in the place of pins touches each other a high electrical current produces new chemical substance (oxides). While the effect related to high current, the low current equipment could also have it after some years of usage. The solution here is to eject the storage from port and to plug in into port and to do it 2-3 times: you will scratch oxide film on surface of all contacts (device’s and port’s for it) to restore pure metal-to-metal touch.