From the public blockchain perspective, the viewer knows that the coins got sent to a new address, but not that that address belongs to the same entity as the sender. They may infer this, but they canโt know it for sure.
Also, while the viewer knows all the addresses from the previous wallet, at most they can infer one address of the new wallet. Every transaction after that is a mystery. So IMO, youโre better off, even if all you do is shift to a new wallet with a keystore you rolled yourself.
There are other things you can do to mildly improve privacy on chain, such as avoiding exact values in either fiat or Bitcoin terms. Avoiding payments of, say $100 exactly or 0.001 BTC etc.
On-chain privacy is its own field of study. People who are serious about it use CoinJoins to obfuscate UTXO history. Sparrow implemented support for Whirlpool, the backend to Samuraiโs CoinJoin implementation, but I havenโt tried it.
Personally, I would say that rolling your own seeds and connecting to your own node is more important.
