Addresses never expires. If tracking invoices is not something that you need, it'll be better for you to just take an addresses from your address tab and give it to the user.

If you want to use invoices, just create but set the expiry to Never. Even if it did expire, it wouldn't matter as the address would still be in your wallet and they're never deleted.

the problem with this method is that it is not clearly defined what it does and the problem with the script is its dependency that was not easy to go through (at least not easy for me). so i would never use it.

that's not how this script and bitcoin core work.
Electrum or any other similar tool use the mnemonic to derive all your child keys at any derivation path you like. this script is just a silly way of deriving the BIP-32 master private key (xprv) then only getting its private key part (first 32-byte of HMAC result) then feeding that as the HD seed used in bitcoin core. then core uses that 32-byte entropy to derive keys at its defined derivation path which if i'm not mistaken is at m/0'/0'

try converting your mnemonic to xprv then decode it using something like http://bip32.org/ and copy the "Key" right below "Chain code" (not the "private key WIF" that is lower lower). then use that in your core as entropy, you should get the same result.

note that i haven't tested this and i'm only speculating based on the source code that i saw. i also don't recommend this method or using any of these sites for generating keys at all. it is too risky.

this is where i looked:
https://github.com/libbitcoin/libbitcoin-explorer/blob/55438a45d9cc20790ca834c1621cfea60d6f4a36/src/commands/hd-to-ec.cpp#L53
https://github.com/libbitcoin/libbitcoin-system/blob/84e8d2a0c6ce4e253669f2f14aedbf74d6b83b1f/src/wallet/hd_private.cpp#L208