"What is special about the ECDH is that your peer's pubkey defines the curve being used, not your secret key!
So if an attacker provides a pubkey from a weaker curve, and you respond with the product of their weak pubkey * your secret, they can use brute-force to factor out and reveal your secret."
https://stacker.news/items/361797
If your signing software is working properly (at minimum using a random non-predictable nonce) your message with signature doesn't leak anything about the used private key. You would need to be able to break ECDSA completely and apparently no-one is able to do this.
You should probably read and understand more of the context of a cited piece of text. I understood, I certainly could be wrong too, the pieces behind your cited source that it's about issues of naive implementations of secp256k1 curve being susceptible to twist attacks when the implementation naively accepts wrong pubkeys which are not on the curve (because they fail to detect this).
I can't quite believe that something like this could be foisted on mature implementations of secp256k1 curve like Bitcoin Core or Electrum use.
You only use their public key to verify a signature that they send you.
Read again and try to understand, also in context of usage with proper software. As far as I understand it, a Twist attack isn't possible with proper implementations.
A twisted pubkey of an attacker should and would be rejected, his signature should fail to be verified. By checking yourself, you don't reveal anything of your private key. Do you understand what DannyHamilton explained to you?