You also said that in the case of 2-of-3 multisig, (three) wallets exchange master public keys with each other, which means any of three wallets will generate exactly the same set of public keys. Doesn't it also mean that wallets don't need the third wallet (seed phrase or master private key) to exist because they already keep the information about its master public key?
Absolutely correct. If you create a 2-of-3 multisig in Electrum, for example, then each of the three wallets will contain one seed phrase and the other two master public keys. This means that each of the three wallets contain all the necessary public keys, and so any two of these wallets can sign a transaction. Even if you lose the third wallet entirely, the other two can still generate new addresses and sign transactions.
Seems like btc doesn't work like eth where you need only 2 of the 3 private keys to recover a multi sign.
No, you need all three public keys.
But the problem is, even if I use they public compressed key to find out the hex value of it which may help me in a way, I don't get all the addresses generated by the electrum.
Turning your compressed WIF private key in to a hexadecimal key achieves nothing useful.
You need to answer the questions we have asked you above:
Do you know if the private key corresponds to a single address you are trying to access?
Are your two public keys individual public keys (which begin with 02, 03, or 04) or master public keys (which begin with Ypub or Zpub)?