I'd like to start with something that's more DB oriented like SQLite both locally and in the browser for example but I understand a documented-oriented approach might make more sense.
There is a fairly comprehensive list of frameworks/tools here: https://localfirstweb.dev/
I work on PowerSync and we did a Show HN last year: https://news.ycombinator.com/item?id=38473743
Also see InstantDB Show HN: https://news.ycombinator.com/item?id=41322281
RealmDB is sort of the goto. They were acquired by mongo which could be a negative signal but the team is solid and I haven't seen it result it much degredation.
EDIT: actually... it looks like mongo may have just announced the EOL for server-side component a couple weeks ago... bad timing!
You'd probably enjoy Triplit then--especially if you're using Typescript.
In that case, there are a number of recent options. https://www.instantdb.com/ and https://electric-sql.com/ come to mind. I wrote about a number of them here: https://digest.browsertech.com/archive/browsertech-digest-tr...