If you haven't already, you need to enable Multi-Factor Authentication on your Google account immediately. Then immediately change your Google account password to a new, strong password.
Likewise, change your password, and if possible enable Multi-Factor Authentication, for every account on every service you accessed while your browser was compromised.
As others have commented, once you've re-installed Chrome and disabled the malicious extensions you probably don't have the persistent threat on your machine anymore. If you really want to be sure, you need to nuke it from orbit: wipe the entire machine and reinstall everything, from the operating system up. That may be painful, and it may be overkill in this specific case, but in many other cases it's the only right answer.
It is unlikely that there is a persistent threat inside the Google Drive web servers, but it's much more likely that the malicious software may have left files inside your Google Drive account that you don't want, or that might be malicious. Go through all the files you have there and remove anything that you don't need.
It is more likely that the malicious software captured information from your machine while it was installed. This could definitely include passwords (which is why you need to change your passwords, see above), but can also include other sensitive information, especially if you accessed that sensitive information while the malware was present. Unfortunately, it's very difficult to determine after the fact what may have been accessed if you didn't have comprehensive instrumentation and logging in place beforehand.
However, none of this addresses the real vulnerability: How did those malicious extensions get installed in the first place? If someone tricked you into installing software that did bad things to you, how can you prevent that from happening in the future? At the end of the day, no amount of software security can protect us from ourselves: we still need to make wise decisions about what software we choose to allow to run. You seem to have decided that Google Chrome is at fault here, and that's a worrying conclusion. Chrome is almost certainly not the problem. Even the malicious extension is not the real problem. The real problem is whatever caused that malicious software to be installed in the first place, and whatever user clicked "OK" when asked to confirm whether to install it.