See the chapter Security and Privacy of the Lightning Network from Mastering the Lightning Network

Not really. All depends how you "organize your stash" on the 3 levels.
https://i.postimg.cc/MTL2kvT0/3level-stash.jpg

Please read these:

• https://darthcoin.substack.com/p/lightning-cleaning-machine
• https://darthcoin.substack.com/p/operating-with-ln-as-a-merchant
• https://darthcoin.substack.com/p/bitcoin-and-privacy
• https://darthcoin.substack.com/p/private-lightning-nodes
• https://darthcoin.substack.com/p/lightning-network-submarine-swaps
• https://darthcoin.substack.com/p/bitcoin-be-your-own-bank-think-like

Lightningprivacy.com

I understand its very difficult to track if you're using unannounced private channels

Yes but It is more difficult if you use your own LN node and coinjoin the utxos that remain when you close the channels.