So i probably now understand that the fees i see in my
https://www.ledger.com/ledger-live software is not the fee related to my transaction only.
That's what misled me. I feel so stupide now

Sorry.
No need to apologize! Everyone starts somewhere.
The fee you see in Ledger live is the fee Kraken paid to miners for the transaction which your withdrawal was part of. However, there were also 20+ other withdrawals part of the same transaction. So Kraken took 0.0002 BTC from you, 0.0002 BTC from everyone else, paid 0.00038385 BTC in transaction fees, and then pocket the rest as profits for themselves.
No, it would not have worked. The Lightning Network is what is known as a second layer, and is built on top of bitcoin. To receive bitcoin over lightning, you must first have regular bitcoin (which you now have in your Ledger), a lightning compatible wallet (which Ledger Live is not), and use those regular bitcoin to open a Lightning channel. This is something you can look in to for the future if you want, but you've done nothing wrong so far.
The reason you paid such a high fee is because all centralized exchanges like Kraken charge high fees.