The “browser console” is a debug and development tool which is designed to show anything you transmit over the line (among other things).
Having your password in a POST request in there is not really a problem. It’s basically as safe there as it was to enter it into the browser to begin with.
Using base64 will only slightly obfuscate your password. For anyone trying to get it from you it’s a non-barrier.
So better to not use it.
What I would do is use established authentication techniques such as for example oauth 2 or OpenID Connect. These would mitigate much of the risks by using time limited tokens that are temper resistant through hashing and/or encryption.