Are there any promising solutions in development/consideration? Or is furthering development of LN the primary approach?
I think LN is still the "primary" approach in the Bitcoin community itself. It has a few problems though, for example the replacement cycle attack, which still make it unsuitable for larger payments.
Sidechain projects and concepts I know of, which are not federated - i.e. centralized management by a static multisig "federation" of users - are:
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Drivechain (problem: needs new opcode, is not well liked by some Bitcoin Core devs)
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Stacks (if everything works well it will be rolled out this year, problem: has a premined token for consensus)
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Nomic (already live, but the peg bridge is limited because it's in an audit process, has also a premined token for consensus)
- Forum user @vjudeu seems to be developing some sidechain too but I think it is still not public.
Federated sidechains are primarily Elements and RSK, which are live already for years.
Then there is the rollup concept, where the data is stored on a sidechain and on mainchain in a compressed form. It already works well on Ethereum, but the popular projects (for example,
Optimism) also have premined tokens. On Bitcoin it would probably also need new opcodes. There's an info website for
rollups on Bitcoin. I read recently that the
Avail project is about to launch on Bitcoin.
There is also the extension block concept, which afaik was implemented in Litecoin for the Mimblewimble privacy technology. It's also a kind of sidechain. It was rejected however in 2017 when it was proposed for Bitcoin as an alternative to a block size increase.
Premined tokens is a problem because it makes the project centralized in some way, there will always be a founder group which is able to extract profits. This is a bit against Bitcoin's ethos, and thus sidechain concepts (except Drivechain) are mostly viewed as "altcoins" by many Bitcoiners. What I could imagine however, as most projects are open source, that you could fork these projects once they work and build a version without premined token.
I think the rollups concept and Stacks/Nomic are the closest to be implemented, and I expect some fully working for this year.