I heard in the early Bitcoin days miners would often process transactions for free (0sat)

There is nothing in consensus rules that says you must pay any amount in fees. But a zero fee transaction may not be likely to get mined. A less than 1 sat per vbyte transaction doesn't have to be zero fee, though.

Your transaction might be 306 vbytes. If you pay 1 sat per vbyte, the total fee would be 306 sats. If you pay 15 sats per vbyte, total fee is 4590 sats.

If you pay 0.5 sats per vbyte, total fee would be 153 sats. You still pay a positive fee, just it's less than 1 sat per vbyte.

Only kinda related, but Bitcoin Core 29.0 adds support for ephemeral dust, where you create a single dust output, but only if the transaction has no fees.