I am using a very very old versions of Electrum. On my cold storage I am running Electrum 2.x and my watching online Electrum is 3.0.x. They still work. Rather not go thru the hassle of having to upgrade to a newer Electrum because then I need to upgrade the dependanices and those I also need to verify to make sure they are not tampered with so I rather just leave everything as is. I'm old school.
However wondering if Taproot will be backwards compatible and will I be able to perform any transactions. All my cold storage is on wallet addresses starting with "1" and none are Segwit or Pay-by-script (start with "3"). I rarely do any transactions so this is why I keep this set up.
As others have already said, taproot isn't going to be an issue for you.
However, running obsolete software on an outdated system might become an issue. There are only five dependencies needed to install Electrum, and you can get away with three if you only want to run it from the source code. They've all been tested to function with the OS, but I suppose there's no way to ensure there's nothing malicious in the code without auditing it. Even validating the packages authenticity doesn't doesn't guarantee that it hasn't been compromised by a malicious developer. I get it, there's no such thing as being too paranoid, until you are.
Here's the list of dependencies needed from Electrum's downloads page:
python3-pyqt5
libsecp256k1-0
python3-cryptography
python3-setuptools
python3-pip
I understand why you're reluctant to update your system, and since you don't make a lot of transactions you'll likely find yourself in this situation again and again. It might be better for you to use a hardware wallet, which effectively gives you the security you're looking for.