Yes, especially do not google the number that you were given on the phone. That is completely certain to turn up the scammer's official looking page and "confirm" the phone number.

I have seen Microsoft support forum articles that list the "Facebook official phone number". The fact that it's not from Facebook doesn't make it less authoritative in a panicked person's mind.

Google, Meta, Microsoft, and Apple really must start publishing an "official phone number". It is perfectly OK that this phone number just plays a repeating message saying that the user should browse google.com/phone. That website can explain that there is no phone support offered, and provide a bunch of links for common scamming hooks that leads to anti-phishing material.