No your funds would still be at risk. There are only a few popular wallets that use seed phrases.
Most wallets use BIP39(https://en.bitcoin.it/wiki/Seed_phrase) but there are some that use different versions or no seed words at all.
Electrum does not ouse BIP39, see their docs explaining why. https://electrum.readthedocs.io/en/latest/seedphrase.html
It would ...
Do I have such a recovery seed?
No. Bitcoin Core does not use mnemonics nor is the seed exportable.
Is there any other way I can migrate my wallet to the trezor? (Other than creating a new wallet and transferring funds from the existing one to this new one)
No. The only way to migrate is to send a transaction that transfers your Bitcoin to your Trezor.
The order is important.
If you have 24 different words but don't know the order, you have to try up to 24 factorial permutations. That is around 620448401733239439360000 different attempts. This may take a very long time and cause you great anxiety, unhappiness and self-recrimination.
Unsure order of 12 word mnemonic
Bruteforcing a seed ...
if I happen to get my 12-words compromised and someone gets to know them, then I would be still safe as long as this person does not figure out which wallet app I used?
Technically, no. The attacker only needs to figure out the algorithm used to convert the passphrase into the public key, which may be used by multiple apps.
But that is probably not what you ...
Sadly if you lost your seed phrase (12 or 24 words) you won't be able to regenerate your private key and get your funds control back. Best advice, look harder where you wrote it or stored it.
PS. Never write your seed phrase in any online place or take any picture, just piece of paper very well stored.
bip39-lib.js works along with bip32-lib.js AND bitcoinjs-lib.
BIP39 is strictly regarding the mnemonic phrase and HD seed.
In order to derive child keys from an HD seed you'll also need to use BIP32.
BUT... BIP32 has no concept of addresses either so ultimately you'll also need bitcoinjs-lib.
In other words you need to use all three libraries to go from ...