Eltoo channel - can opening be off-chain In Eltoo the set-up phase is similar to Lightning. You fund a n-of-n multisig (usually 2-of-2). Of course you don't want to publish this until you have a bail-out possibility - called "settlement transaction" here.

But what I found out is this "setup transaction" is exactly the same as later "updates" - you could also call it Tu0. So is there any need to even broadcast this first transaction to the blockchain (before doing further ones)? Or is it enough if both parties just keep the properly signed Tu0 (with both signatures)? What else do you need in case of an uncooperative close? You broadcast Tu0, latest Tui and (time-locked) Tsi ?
I guess one problem would be the other party trying to "double-spend" his input into the multisig?
I think you have answered your question yourself in the last question that you raised. The problem with not publishing Tu0 is that the funder of the channel could double spend the input of Tu0 and in that case "steal" all the money from the channel. so with eltoo we still need the bitcoin network / blockchain give proof of the existence of funds in the 2-2 multisig