I'd like to transfer my BTC funds from my old (Ledger) hardware wallet to my new one, but I don't quite know how to go about it.
I hope your new HW wallet is not Ledger again.
Should I connect the ledger wallet to my node for the transfer as well? Or is only connecting my new HW wallet safe enough?
I'm not sure what exactly you mean here.
You need new addresses, from the new HW. After that, you definitely need to access your old Ledger wallet to send BTC to the new addresses. There is NO difference compared to sending anywhere else, here only you know that it is your new HW wallet.
Should I send my BTC to different addresses in the new HW wallet, or is it safe enough to send them all to one address?
It also depends on the quantity you have and your later needs, but I guess it's better to send everything to one address. He could use the transaction as a consolidation of funds if they were collected from several smaller transactions. It has nothing to do with safety if they are in the same wallet
All of my BTC is KYC. Does this mean that I lose my extra privacy that I got with my node, by doing transactions through my node?
If your coins are already "KYC" as you say, you've already lost your privacy there. If such a status suits you, then it is enough just to move the coins and there will be no significant changes in that matter. Anyone who knows that your address is A and all the funds on it is yours will certainly know that you sent them to address B and it will be easy to determine the connection of those addresses with your KYC information.
In case you want to increase the privacy of your BTC, then when moving from old to new HW, use one of the mixer & tumbler services.
Be sure to ask here before taking any more serious steps if you are not sure, it's better that way than to feel bad for you later.