It's not just power, if it where, they'd fit a USB C rechargable cell in there.

Its still a cheap casio resin watch at the end of the day. If this where to be able to push/pull notifications, the watch would be completely different in cost, ui, marketing, etc.

It would go from being charming retro tech with modern features, to dime a dozen bloatware/fitness tracking hardware.

I'd argue the coin cell and the power budget limitations that come with it are part and parcel of it's nature as a cheap casio resin watch.