I created a wallet with atomic and wrote down the 11 words that make up the pass phrase. Next I scanned my fingerprint for ease of use. It also, separately, accepts a password to unlock the wallet. I went to BTC, I clicked on receive. It generated an address for me to receive some bitcoin. I could copy and paste that address into the coinbase form where it asks for an address.
In theory the wallet on my phone should be secure (not leaking the pass phrase). In theory it should be safe from loss, I should be able to install the same app on another phone, type in the 11 words and get all my keys back. I can print the 11 words and put the paper in my safe.
It's considered more secure than private keys. But is it really? Private keys can be leaked or stolen, but so can the 11 word pass phrase (in theory). It is considered more secure for transactions and I agree. Reusing the same address for multiple is considered a weakness and that's what happens when you store a private key. I do private keys mostly and am not too concerned.
Is is safer from loss? No, a private key in a paper wallet in your safe is as safe from loss as a paper with the 11 words printed on it.
Thanks for the additional info...”self-custody” is a bit more complicated than leaving your BTC with an exchange/Coinbase!
My primary concern with your “import private key” methods is that you don’t want to have your private key known by Coinbase (theft...Coinbase generated your private key & could use it for nefarious purposes if they wanted...I have “trust issues” ;-)). Also your old Coinbase transactions can be easily “trackable” by the government or others with the old private key/public key transaction addresses. A fresh private key from a new wallet prevents this...generate a new wallet then send/transfer your BTC to the new unadulterated wallet/private key. (And DO NOT reuse public key transaction addresses from your new wallet for maximum privacy...one use per address). If really paranoid then use a “whirlpool/bit-mixer” to obfuscate/privatize the BTC that came from Coinbase:
https://bitcoinmagazine.com/guides/how-to-whirlpool-bitcoin-on-mobile
https://coincheckup.com/blog/bitcoin-mixer/
If you want to help support the BTC network (you are an official “node” of the BTC network) and “mine” BTC you can use the original/first/”OG” Bitcoin “Core” software to make your new/fresh BTC private key/wallet...(it will download the whole Bitcoin blockchain ledger of BTC transactions back to 2009 tho...takes a long time unless you have a real fast Internet connection...currently 578 GB!)
https://bitcoincore.org/en/about/
https://bitcoincore.org/en/download/
Your odds of mining a BTC “Block” by yourself with BTC “Core” (you get over 3 BTC) is exceedingly low tho...best to go with a BTC mining “pool”:
https://cointelegraph.com/news/bitcoin-halving-2024-completion-confirmed
https://www.hedgewithcrypto.com/best-bitcoin-mining-pools/
https://99bitcoins.com/bitcoin-mining/pools/