I tried to log on to my Gmail account this morning and I got a message that I had to change my password. I don't know exactly why that happened, but I think it's because I had cleared my browser history the day before, How can I do housekeeping without deleting my passwords?
Be careful with those emails asking to do anything to keep access to your account as they usually are scams / phishing attempts.
Bear in mind that passwords are not stored on the web browser cookies / cache but some web browsers like Chrome could save them in a special storage space. The cookies that could be deleted are those that save information about your account session and those that identify your device as a trusted one (I'm not sure if Google is still using the last ones).
Please follow the suggestion of [Make your account more secure] https://support.google.com/accounts/answer/46526?hl=en Note: I'm leaving the URL visible so you can very easily see that it's a help article hosted on Google servers.