I made myself a Electrs server and have connected my wallet to it. The purpose of making the server is to make my transactions private - is using my old wallet with the server then pointless?
This is not a question that can be answered simply with a yes or no. The answer is depends. What do you want to do and from who are you trying to hide? Node operators, transaction tracking, government and other observers?
I guess the question is should I make a fresh wallet, connected to the server from the start? Send my funds to a new wallet, and start anew?
If there is no strong reasons for keeping the old wallet, I regularly recommend swapping spending wallets. Having a very old wallet may feel nice for vanity's sake but it is a privacy nightmare. If your machine ever gets compromised in any way, a very long history about you will be exposed.
Couldn't that transfer to the new wallet be tracked also?
Of course, that is the basic of how a blockchain works. You will see this transaction on the explorer. Address 1 or multiple addresses (old wallet) -> Address 2 (new wallet). As I said it really depends on who you are trying to hide from. Running your own Electrum server
provides you with the opportunity of keeping your transactions separate and private,
not a guarantee! You need to use Coin Control carefully in a privacy preserving way. If you don't all I need to know is 1 address from you and I can just go to
https://blockstream.info/ to find the others out.