Afaict, SIGHASH_ANYPREVOUT will get activated anyway to enable stuff like eltoo. Then drivechains will be possible too. Just a matter of time as I interpret the consensus behind it.
So no specific soft fork required for drivechains.
For the BMM/BIP-301 part, again the surface is very small, but we arguably do not need that at all, since anyprevout (once that is merged) enables blind merge-mining in way that is probably better than BIP-301, and that soft-fork is also very simple, plus already loved and accepted by most of the Bitcoin community, implemented and reviewed on Bitcoin Inquisition and is live on the official Bitcoin Core signet.
A drivechain uses BMM for consensus. But the other important part of a drivechain is the hashrate escrow, which controls the transfer of BTC between the drivechain and the mainchain (one implementation of hashrate escrow is BIP-300). APO can do BMM but cannot do the hashrate escrow.
I think that it's always been possible. There just isn't a market need for it. Sidechains were BEFORE forks, for those who don't know the history.
Ordinals became possible with Segwit also. Took years for that to finally get implemented and where is it now? Seems like this garbage has turned out to not be worth anything, and I'm sure the miners all thank you fools for backing them up in the hardest part of the 4 year cycle.
SIGHASH_ANYPREVOUTwill get activated anyway to enable stuff like eltoo. Then drivechains will be possible too. Just a matter of time as I interpret the consensus behind it.