As far as the as what I might do:
1.) Try to see if I can use the ledger with the old firmware on electrum.
or 2.) go to the air gapped computer and create a new wallet from the ledger seed.
your problem is about front-end software, even if the firmware is old, don't worry.
I do not know how old your firmware is, but this post is for Firmware 1.0.0
https://www.reddit.com/r/ledgerwallet/comments/m4pk7q/successful_recovery_of_btc_from_a_hw1_ledger/, and I do not know why you do not want to update the firmware, since the recovery service does not pose a danger to you if your goal is to move to a new wallet, but nevertheless, using old firmware on electrum is enough to solve your problem.
For ETH I think MyCrypto (NEW) will work fine.
Create your airgap wallet and create a new wallet and transfer your Bitcoin there, because importing a wallet alone doesn't increase the security of your wallet. Leave your Ledger device including the seed phrase.
So as I explain above part of the difficulty is in doing the transfer. AFAIK to transfer from ledger I must upgrade firmware, which I prefer not to do.
No, you don't need that.at least for now.