Good points. I am not an expert on Lightning but the CEX (Kraken) knows you withdrew to Muun, right? (It can see the path and where the Lightning ended – someone correct me if I am wrong).

Hence the CEX knows you withdrew to Muun, and then Muun knows your cold storage address (since they have a record of your incoming LN, swap, and outgoing tx).

If the data from the CEX and Muun both leak or are provided to 3rd parties, you might still be connected to your coins. But I understand that is highly unlikely, if at all possible.

I like to do at least one more hop in LN in order to obfuscate the movements of funds a bit more (e.g., withdrawing LN to my own node and then sending it to Breez to use Boltz for swapping – good thing is Breez has Boltz integrated). But this might be too much.

If your solution with Muun works, I guess it is fine. You are not keeping your coins on Muun so you do not need to worry how they do things, you only care that they work for a few minutes for you to make your transactions.

If Muun is using submarine swaps to imitate LN, it is their problem and the economics of transaction fees will either allow them to do it (and there is not problem then) or it will force them to change this practice.