Yes, it depends on the route that your payment had to take to reach the receiver's channel.
The total fee depends on the number of channels that it went through and their respective routing fees.
The more expensive channels that it need to hop into, the more fee that it'll accumulate.

The sent amount is quite high too, it may have been broken-down into multiple separate small amounts to send the full amount.

In terms of those hard-coded trampoline nodes, those have different connections to the lightning network
so it could be cheaper if one has shorter route to the recipient and has active channels to nodes with lower routing fees.
But finding which one will total a lower fee requires intensive research (for the indications above) or testing.

The only way I know is to open a channel directly to the recipient's node.
It's recommended if it's an exchange's lightning node where you would deposit and withdraw bitcoins frequently.
Usually, exchanges with lightning deposit/withdrawal option have a note with "connect to our lightning node" message or similar.

I'd expect LN to be used for small transactions. This is worth more than $1000, and I would keep such amounts on-chain. But: I've seen exchanges that support LN withdrawals, and it's either free, or something like 5 sats. So that makes me think they don't pay high routing fees.

I've used several LN wallets in the past, but never this one. Does it at least show you the fee before sending the payment? You paid 0.6% fee, which is a lot. From what I've seen, most LN node owners "complain" that they don't make any profit. It sounds like the only route for your (high) payment was through a node with much higher fees than average.

I can't really tell you how to avoid this