I use a password manager with a long rememberable master password for logging into all of my online accounts. When signing up for new accounts my password manager prompts me to generate a strong password which it then autofills. This auto generated password is a twelve character long alphanumeric string. Is there higher risk in me attempting to generate a random password by randomly pressing twelve characters on on the keyboard vs a potential flaw in the generator that would allow password discovery with some other available information (password creation time, password length, creation method)?
I know in the ideal case the password generator is far superior to my attempt to be random on the keyboard, but is my hand dropping on the keyboard so much worse that the risk of my password manager's generator being flawed is the better of the two options? I know this might be an opinionated question so any facts, studies, or personal knowledge on this topic would be highly appreciated. I did attempt to Google this question and my searches along the lines of "password generator vs random typing" yielded no good results.
PS: Where as I don't use them it might be cool if answers also addressed random typing vs going to Google, searching "password generator", clicking one of the top results, and then using a web based random password generator.