I am now affraid to provide my information to third party because google that is not safe to use warn me about my twitter account password that has been compromised recently
It is different on your compromise. If the compromise happened directly on Twitter. Hacker changed your Twitter account's password on Twitter, Google has nothing to do and you can not say it is their failure to warn you. Twitter failed to warn you on the compromise instead.
If hacker reset your password in email (I am not sure the process to reset password with Twitter). It is the failure of Google if they did not send you warning that new log in on your gmail with strange IP address.
I do not know if this is true but I believe it can not be lie, I changed my twitter account password immediately.
It is good but did you use 2FA for your Twitter account?
I have forgotten that I back up on google, I removed the back up immediately because of what I learn from our forum bitcointalk that it is not also safe to have back up online.
You did good step but it is not enough.
To be safe from online threats or data leaks from companies, the best you can do is Never store your identities, backup details online, on their services. If you did it, I doubt that you can completely clear all traces of your data on their centralized services.
Do you notice that Google docs, sheets, etc. have features for you to check past updates, previous versions and restore it?