Hmm, looking at my old notes here I wrote down a 12-word combination under the title 'ELECTRUM', so I'm pretty sure that's the seed, but you say 16 secret characters? Not words?
The 12 words seed phrase is enough for the recovery if you bypass the 2FA.
But if you do not need to bypass the 2FA, you will the 2FA backup code which are 16 characters. Also you you are able to have access to your wallet and be able to spend from it after the upgrade, just the 2FA can be needed to move all your coin s from the wallet. But if you have the seed phrase, you do not need this.
Edit:
Google 2FA can be back up online. Did you do that? Use your gmail on the phone you used maybe you backup the 2FA online. This is not advisable and not secure, but maybe you did it. The secret codes are best for backup and it should be offline.
Unfortunately, I haven't...
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Not unfortunately, it is not secure and not recommended.