From Matthew Cederquist, Game Producer for Diablo II:

“Yes! Keep your old save files,” said Cederquist, when asked about a save file importing feature. “Back when we were working on [the remaster], we wondered if the old save files would work, so we kind of shoved it in, and it worked! So yes, your local singleplayer save files will carry over.”

Now I just need to buy a CD drive to access my old backups. And to anyone thinking, "Who still has their backups, sites like this still exist. Never underestimate Diablo II players.

Diablo II Resurrected Will Let You Import Original Diablo II Save Files
We hope you have a backup ready.