Basically, all that's going on is that Keep seems to be continually calling chrome.browserAction.setIcon [1].  Most of that flow is the normal extension API method route - the renderer dispatches an IPC method, which is received by the ExtensionWebContentsObserver, and then routed to the proper ExtensionFunction via the ExtensionFunctionDispatcher (lemme know if you want code pointers to these, or to chat over gvc for a few minutes - it's a little complicated, but 99% of extension functions take this same flow).

Once the browser action icon is updated, we dispatch a notification, and redraw the icon.

Since the icon isn't visually changing, it seems like keep shouldn't be calling the API method as the first and most important fix.

On the chrome side, there are a few things we could do.  One would be check to see what the current icon is - if they're specifying the icon by path, we might be able to just do a check to see if it's the same path as was last set.  Otherwise, if it's pure image data (as from a canvas), it's potentially possible that we could do a bitmap diff to see if anything changed.  Unfortunately, that would slow down the common/good use case (when the API is only called as-needed), but it would obviate a bunch of churn if the icon is in fact the same.  (However, at some point, there's only so much we can do - if there's a pixel difference and it's just imperceptible, we'd still update the icon.)

[1] https://developer.chrome.com/extensions/browserAction#method-setIcon

Is there anything we can do to fix this aside from reaching out to the Keep team?

I had as a to do for a long time to file a bug against Keep for excessive updates, but when I finally got around to it I could not repro. Assigning to myself to check again - I'll either then file a bug against Keep or close out this one.

Last time I checked the issue no longer existed.