PSWD, the most comprehensive password generator for iOS, gained Shortcuts app support with version 1.3. macOS version also supports Shortcuts, with version 3.0.
Using the Generate Password shortcut, you can immediately generate one or more passwords using any preset you create in PSWD, including the dynamic Current Preset setting, which includes the latest configuration from the app. This shortcut returns the password as text and you can pass it onto any other shortcut that accepts text as an option.
For example, you can create a shortcut that copies the resulting password to the clipboard. When you add this shortcut to the share sheet of iOS, it gives you the ability to generate a password on any app that has share sheet support.
You can download PSWD on the App Store.