there are many password manager extensions and in built password managers in browsers are available. I signup on any sites also related to finance it shows an option of save passwords.
i click the save password button when the site is non financial or not very important or risky for me (like social media, etc).
but when i login to binance or online cypto wallets and banking sites, then i don't click on save passwords because of fear of password may be known by google, brave, or any browser.
I don't think password managing extensions are safe, but i think big companies know everything from billions of dollars worth wallets password to out privacy.(maybe i am wrong in password matter)
so these type of saving passwords feature is safe, if yes or no then please explain it.
better to avoid any type of browser extension whether we are talking about a password manager or something else. Extensions may contain vulnerabilities, phishing or collect user data, better to rely on a solution like bitwarden and if you can do self-hosted even better or keepass which saves your passwords in an encrypted local, remember however to make a backup for both.