Once taproot is implemented for channel openings, I imagine it'll hide the information currently visible such as the fact it is a lightning channel and that it is a channel e.g. between Mangoo Tree and Aare Bank?

No it won't actually. That information isn't in the blockchain. What's happening is that mempool.space is running a lightning node, and collecting the gossipped public channel information. Public channels reveal what txout is associated with the channel.

That's one reason why private channels exist!

Ok got. Thanks for the clarification.

Sounds similar to what Amboss announced doing, i.e. report on the channel balances information they gather through their platform and LN gossip, no? I might be wrong on the specifics (Amboss, the means to achieve it,...).

Well, if it's permissionless, they are allowed to do it. I guess privacy improvements will have to come from development efforts to control this depending on one's needs.

In fact, mempool.space also provides information on Lightning channels and nodes now, just like Amboss.

In the future there will probably be ways to remove Lightning channel txout information from the public lightning channel info. But that isn't trivial to implement as lightning uses the fact that you need to create a txout as an anti-spam mechanism for the gossiped channel info.