Like a rollup, segwit transactions put the new state (i.e. recipient & amount) on the "main" blockchain. On a rollup, the authorization for this new state goes in a separate blockchain. In segwit, that proof is a signature and it goes in the witness data.

The witness data for every bitcoin block is committed to in the main blockchain just like how rollups are (I think?) committed to in the main blockchain, and, like rollups, people who don't use segwit (the rollup) don't have to download that extra data. Like rollup txs...

...segwit transactions are also cheaper than "regular" (i.e. non-segwit) bitcoin transactions because they put a minimal amount of tx data on the "main" blockchain (which is more expensive to use) and put the majority of tx data in a separate structure that only segwit users see.

If there's nothing missing from my analysis (I suspect I'm wrong though), then segwit is a rollup, so those who want to see rollups on bitcoin: consider taking a step back and be thankful that we already have one, and we've had one since 2017.