There is no need to back up your master private key or individual private keys from an Electrum wallet.

You could use any old copy of Electrum software to restore an Electrum seed phrase and extract the relevant private keys. Even if the devs abandon the project, the GitHub disappears, and your own devices are destroyed, there are thousands of people who would pretty quickly upload copies of the Electrum code for other people to download.

Even if no one did that, you can use any open source piece of software with two very minor changes as explained by pooya87 above to restore an Electrum seed phrase. For example, with https://github.com/iancoleman/bip39, simply open src/js/jsbip39.js, change line 116 to return true; and at line 144 change the word "mnemonic" to the word "electrum". The derivation paths will be different (m/0 for legacy and m/0'/0 for segwit), but it will generate your Electrum addresses just fine.