If I buy bitcoins from a legitimate exchange and put them in the Electrum wallet is that wallet now forever linked to me by this transaction?
The government can verify your identity on the trading platform " legitimate exchange" and then link that address "not a wallet" to your identity.
Customizable, powerful computing enables them to track all the currencies sent from that address to the rest of the addresses of the Bitcoin network.
Using a mixing service "based on mixing service" will enhance your privacy but does not mean it can not track you.
Bitchin is not built for high-privacy.