A custodial wallet e.g. Binance, Kucoin, Coinbase will not give you their private key and if their company shutdown, you don't have any way to recover your coins which you leave there.
A non custodial wallet which use BIP39 code without add anything e.g. Electrum, Bluewallet, Mycelium will let you to recover your coins, even the site was been shutdown, although it's highly unlikely.
The tricky part is a non custodial wallet, but it's a multisig wallet e.g. Muun wallet and Blockstream wallet, you can't recover your wallet in other wallet, only in their own site.
Muun is a multisig wallet with lightning support, so backing up a mnemonic alone would mean your bitcoin could be easily frozen. Self-custodianship is at the core of everything we do, so this wasn't acceptable. We built an Emergency Kit that gives you full self-custody of your money when combined with your Recovery Code[6].
Your Emergency Kit is a PDF document with the information and instructions needed to find and spend your funds independently. No need to brute-force any missing data. Everything is there, including your private keys and output descriptors[7].
As a hierarchical deterministic wallet, Blockstream Green uses the BIP32 standard to derive the child keys for its wallet.
Although Blockstream Green uses industry standards for recovery phrase generation, wallets created in Blockstream Green using Multisig Shield cannot be restored on other wallet software. This is due to the unique multisig security model used for Multisig Shield wallets. In comparison, wallets that use Singlesig can be restored on most other wallet software (e.g. Electrum).