My question is, does coinbase know and keep track of who I am sending bitcoin to with the mobile coinbase wallet? Should I consider another wallet?
You will find this thread interesting:
Is Coinbase noncustododial wallet recommendable?That is the noncustodial wallet you are referring to.
https://wallet.coinbase.com/privacy-policyInformation We Collect
We receive or collect information when we operate and provide our Services, including when you install, access, or use our Services.
Information you provide
Your Account Information - In order to create a Coinbase Wallet account, you will provide us with a username. You may also voluntarily add other information, such as a username.
Your Transactions - Your Network private key, which you utilize to access your funds and initiate transactions, is stored only on your own device. However, to facilitate your transactions and provide you with your account balance, we store the Network public key address associated with your Network private key.
Customer Support - We may collect additional information you may disclose to our customer support team.
Information we collect from our affiliates
Our "family of companies" is the group of companies related to us by common control or ownership ("Affiliates"). In accordance with applicable law, we may obtain information about you from our Affiliates as a normal part of conducting business with you, such as when you link your Coinbase, Inc. account to your Wallet account, so that we may offer our Affiliates' Services to you (e.g., convert cryptocurrency into fiat and make withdrawals into your bank account).
Automatically collected information
Metrics and Performance Data - We may collect service-related, diagnostic, and performance information. This includes high level information about your activity (such as how you use our Services and how you interact with others using our Services), and diagnostic, crash, website, and performance logs and reports.
Device and Connection Information - We may collect device-specific information when you install, access, or use our Services. This may include your IP address and, if you choose to allow push notifications through Coinbase Wallet, your device's unique push token. We may also temporarily collect information about decentralized applications (dapps) that you are connecting to, while establishing that connection.
Status Information - We may collect information about your online status on our Services, such as when you last used our Services (your "last seen status").
Use Electrum,
https://electrum.orgFor privacy, use
https://bitcoincore.org/en/download/ with Tor, but you will have to download appropriately 400 gigabyte of blockchain.