I really liked this run down of privacy in Ark (I think it helped me understand Ark a little better, which I had gotten rusty on because I haven't been paying as much attention to it lately).

Here's the summary:

I think the privacy afforded by Bark maintains a nice balance between privacy and usability. When used within the normal operating model, the ASP has no more insight into your transactions than the average wallet enabling on-chain transactions (so excluding wallets connected to one’s node). It’s also not too different from most consumer lightning wallets that use an LSP as the network gateway, although receivers can still have better privacy in lightning. All in all I think Bark seems to pay attention to privacy while not letting it bog down the user experience and I’m hopeful they’ll continue to uphold this standard.

The Ark Service Provider has a lot of insight into your transactions...but this is not so dissimilar from something like using Phoenix or an onchain wallet without running your own node.

I think cashu provides better privacy from the mint operators, but @1440000bytes has done some interesting research on this (and also on Ark privacy: #1455970).

Whatever the case, the article is a nice quick read that explains a lot of the mechanics of Ark from a privacy perspective.