How is blockchain relational?
I do not think it is.
Blockchains are meant as a data store. Archival, verifiable. But not easily searchable. There is no design on blockchain for advanced query languages/logic.
It seems like the OP is going after something like blockchain that adds querying. But I don't think blockchain syncing is designed well enough for client-side use, and the OP seems to want to use this database client-side in JavaScript. I think it would be possible to implement blockchain syncing with WebRTC, but WebRTC has some security risks for users (IP leakage mostly) so I am not sure I would start off with that as a primary communication channel.
Most blockchain clients have a DB with a cached version of the chain. This is typically done with a typical, off the shelf DB. For example Bitcoin Core uses LevelDB, but other implementations use SQL lite.
As I said at the end, blockchain isn't really what OP wants. It meets his requirements mostly via technicalities.
Sounds like he wants a blockchain?
A blockchain probably isn't really what OP wants. But funnily enough it does meet all those criteria.
> what I’m after is a database to be embedded on client-side applications itself, be it desktop, browser, mobile, etc. Thats how most Blockchain clients work - on the client side, with APIs (usually RPCs) to chat with other programs
> Being immutable means that only new information is added, no in-place update ever happens, and nothing is ever deleted.
Immutability is exactly what blockchains were designed for.
> Syncable
Since blockchains are decentralized by nature, this also comes out of the box.
Of course if you choose a blockchain you have to deal with a host of other issues... performance, no SQL (in most clients), harder to debug, etc. But still a fun thought experiment