Probably because the steps are quite hidden, here's how it can be done:
- After Opening Electrum, if there's any existing wallet, it'll prompt you to type the password.
- Do not type anything, instead, tap outside of that window and you'll directly enter Electrum GUI without any loaded wallet.
- Create a new wallet, in the last step, you'll be prompted to set a password that can be different from other wallet's password.
- After having two wallets with different passwords, the "unified password" feature will fail its initial check and set that your existing wallets and new wallets can have different passwords.
I just tested this and I confirm that it works! If you don't enter a password when your first load Electrum, you can create or recover a different wallet and create a unique password for it. The next time you open Electrum on your phone, it will still prompt you to enter a password. You can but you don't have to do that. Click outside of the window again like nc50lc explained, click the Open/Create Wallet button, select the wallet you want to load, and enter the unique password you have set for that wallet only.
Thanks nc50lc!