Or copy full-chain membership proofs*

Monero's next major upgrade that does away with ring signatures and puts its privacy about on par with Zcash. I'm not 100% certain about the performance differences compared to Zcash tech, but fairly sure Zcash is still more burdensome to process by a significant margin.

If you think many sidechains could scale, why not simply scale by using different crypto that already have these desirable properties? Each with their own trade offs/use cases (the same way Litecoin usage spikes when Bitcoin fees are high). The only difference between them would be that sidechains are pegged to Bitcoin price ostensibly. But for short/medium stretches of time that could also be a bad thing.

Building out atomic swaps, DEXes, and UX/UI around them will continue making this easier and cheaper to do

With the ongoing anti-sidechain sentiment from maxis I feel like it will be such a long shot getting sidechains onto Bitcoin...on top of also trying to capture existing network effects of every crypto that is copied. I'm all for more options, and wish you luck, but it just seems like swimming upstream from where I'm sitting.