I was looking into this a bit because of the SN Spark Wallet. (I don't follow the chatter, but I try to look into whatever service I use before I start using it).

The claim of unilateral withdrawal on Spark is fairly technical surrounding the creation of timelocked multisig transactions. But I came away with the thought that under certain network conditions, unilateral withdrawal is indeed feasible. But it depends on your software implementation to properly store and broadcast that transaction in time. I think you need to trust the L2 network's watchtowers too.

Based on my understanding of the Liquid hack, there's likely a disconnect between what the software implementation shows as your available balance and the underlying timelocked transactions that make up the unilateral withdrawal claim, i.e. the sum of the displayed wallet balances exceed the sum of the unilateral transaction claims.

All this to say, the trust assumptions are extremely technical. If you don't understand it, you should probably treat these L2s as custodial. Even if you do understand it, you'd understand that the self-custody claims only apply under certain technical assumptions and conditions.

but clearly you can't do unilateral withdrawal because the network is paused right now

That's where I'm a bit confused. As I was reading into Spark, my understanding is that you should have a signed multisig (unbroadcast) TXN that you can broadcast to the mainchain in order to initiate the unilateral withdrawal, in a way that doesn't depend on other Spark counterparties. Not sure if Liquid works similarly. But again, it depends on either you knowing how to broadcast this TXN, or your wallet software being able to.

That's my (limited) understanding, anyway.