Despite TeraCopy has a better GUI, it actually faster than ltfscopy.
The ltfscopy simply calls other program like copy (on Windows, or cp on Linux), then call md5sum twice to get original file hash and target file hash, all in sequence. Which I think you can calculate the hash when you copying it, or just calculate the two md5 checksum at the same time.
With a 330GB file, my SSD can read up to 300MB/s, and LTO6 tape drive can read up to 160MB/s. I can save ~18 minutes just by doing it smarter.
PS: TeraCopy do support SHA3-256 but it can only handle ~80MB/s, which is a huge shame. I have to use Blake3 to speed things up.