If you want anonymity, it is better you connect your Electrum with Tor, and that should not be when you are making transaction but anytime you open the wallet and doing anything on the wallet including while making transaction.
You have full control on your coin while using noncustodial wallet, you can use anything like Tor, VPN to mask your identity.
You mean blockchain.com wallet, right? That's not a safe way to store or manage your cryptocurrency because blockchain.com is not an open-source and is controlled by them, i.e. by 3rd party. Never make yourself dependent on 3rd party when you decide to store or manage your cryptocurrency.
Blockchain.com will generate users seed phrase, which means the wallet is not controlled by Blockchain.com but users, you can import your seed phrase on another wallet and you will have access to your coins and be able to spend it. But it is true that the wallet is close source and this makes my comment not to be entirely right because we do not know the wallet source code and we do not know there is a backdoor.