What makes a password strong
Strength comes from unpredictability, measured in bits of entropy. A password drawn at random from 94 printable characters gains about 6.5 bits per character, so 16 characters give roughly 105 bits, far beyond what any offline attack can search. Length matters more than adding one more symbol: going from 12 to 16 characters adds more strength than any character rule.
The other half is the randomness source. This generator uses the browser's cryptographic random number generator (crypto.getRandomValues), not Math.random(), and guarantees at least one character from each set you enable.
Passwords vs passphrases
Random character passwords are best for anything stored in a password manager. Passphrases, several random words joined by a separator, are easier to type and remember, which makes them a better fit for the few secrets you have to type by hand: your password manager's master password, a disk encryption key, or a Wi-Fi network. Four random words from a large list already give more entropy than most people's "complex" passwords.
Options that help in practice
Exclude look-alike characters (0, O, I, l and 1) when a password will be read aloud or typed from a screen. Turn symbols off for systems that reject them, and make up the difference with extra length. For passphrases, choose the separator and capitalization a site accepts.