The important point is that inserts for aluminium (polished sharp edge, high rake angle) reduce tool pressure which reduces the forces on the machine allowing a small machine to do more than it could before, and they will cut tool steel just fine.
The inserts I'm using are from DASAN official alliexpres store (no affiliation, not sponsored, just who I use) https://www.aliexpress.com/item/32917...
$12.50 AUD (~$8USD) for 10
For my friend's mini lathe he got a set of tiny, 8mm shaft, insert tool holders (with Al inserts) from here (no affiliation, not sponsored) https://www.aliexpress.com/item/10050...