Thunderbird prior to the completely re-written version 78 provided encrypted GPG/PGP email support via the Enigmail plugin.
Sending encrypted email used both your public key and the recipient(s) public key(s). This was easy to see simply by selecting the sent email. You would be prompted to enter your own Private Key to decrypt the sent mail, or you could look at the message source and see the -----BEGIN PGP MESSAGE----- content.
Thunderbird 78 is a complete re-write and no longer uses Enigmail or GPG. It now uses a subset of OpenPGP.
It still includes both your public key and the recipient(s) public key(s) but it's less easy to verify, you'd have to open the email via an editor outside of Thunderbird 78 to see that the sent copy is indeed encrypted.
So what's going on with Thunderbird 78 and the OP's question, "Does Thunderbird store an unencrypted copy of the emails anywhere?"
No it doesn't store unencrypted email, it stores your Private Key and auto opens everything!
Now it gets even fuzzier.
The New Thunderbird developers will tell you that the stored Private Key is encrypted, and it is, but it's automatically accessible via another key stored in the Thunderbird database, in the clear.
The next level of fuzz is that the official line here is that if you use a master password then the database is protected by the master password. This is true, but this means all of your private keys are protected by only the same master password.
The net result is that Thunderbird 78 automatically opens all your encrypted mail because it has all your PGP secret passwords. The developers insist that this is for search and sort convenience and is what users desire.
By contrast, Enigmail never writes private passwords to disk, they exist only in your head and in RAM while being actively used. Additionally opening one key does not open other keys.
Interlink is a Thunderbird XUL based fork. It supports Enigmail and Lightning plugins. You can even drop your current Thunderbird profile (Pre-78) into Interlink and be instantly converted over. It runs on Linux and Windows.