The threat is that Google (perhaps forced by the NSA, perhaps only for some users) modifies Chrome to include code that logs all keystrokes or specifically detects the Signal extension (or standalone app if Chrome is also installed) and uploads the plaintext of all messages to Google or to the NSA.

In other words, you have to trust Google to not insert such a trojan by itself and to not bow down to the U.S. government should it try to secretly force Google to do so.

You also have to trust that their security is good enough to prevent third parties from covertly performing such a feat.

That's not say that Google should not be trusted or should be trusted less than other parties, but that's the threat.

Google adds Google Analytics to their browser, to automatically report what a user does in Chrome apps, and "accidentally" your whole chat history ends up on Google’s servers?

This is not an unrealistic example.