Your login password is used strictly to after it has been locked due to inactivity or being closed.
When you first download the MetaMask extension, you will be prompted to create a new password after importing or creating a new wallet. Securing your Secret Recovery Phrase and password metamask wallet login password
The password is stored only on your local machine or mobile device. Your login password is used strictly to after
MetaMask uses your password to derive an encryption key that secures your Secret Recovery Phrase (SRP) and private keys on your device. How to Create or Change Your Password metamask wallet login password