zSide would definitely need its own network effects, but the softfork includes an upgrade to Bitcoin Core that has a sidechain section. So you can click on the sidechains and choose whichever you want. There’s a maximum of 256 (though you can have sidechains of sidechains so no real limit), and they sort of act as the "official" Bitcoin sidechains. With atomic swaps, anyone can use any sidechain and it’s all Bitcoin.
zSide is actually much cooler than zCash for fungibility. In the diagram below, Paul shows how he’s merged zCash privacy with a deniability method that he created. Deniability doesn’t even require a softfork. Unfortunately, no wallets have implemented this feature.
https://www.truthcoin.info/blog/deniability/
I’m sorry, I don’t know where I got the idea that BMM is for the peg-out. In BMM, a sidechain miner would use RandomX to mine a block, and then send a request transaction to Bitcoin miners that includes a special hash. If they mine the block (and they will because they’re blindly looking for blocks with the most fees) then they receive BTC. It’s a bit complicated, but makes it easy for Bitcoin miners to ignore. 