When you say simplified code it's hard to tell where you are going wrong.
Here's an example of how you can derive a bip44 key pair from a mnemonic using bitcoinjs-lib v3.3.2
let mnemonicInput = 'width bicycle axis tell burst outdoor tray episode where they forest meadow enhance twin focus';
let seedHex = bip39.mnemonicToSeedSync(mnemonicInput).toString('hex')...
if I generated 100 addresses and transferred some BTC to all of them, I need to backup all the 100 addresses.
Bitcoin core is an HD wallet. So you should only need to backup the extended master private key shown at the top of dumpwallet.
# Wallet dump created by Bitcoin v0.21.0
# * Created on 2021-05-05T17:57:09Z
# * Best block at time of backup was 627544 ...
Open source Shamir BIP39 implementation in C# (use with usual caution).
Slip39 mentioned earlier is NOT backing up your seed, but the derived master key. From that it is impossible to get the seed back.