brent I can remember when I started with Solus, I had Chrome installed as a third-party program, I think you needed to make a special check to update third party programs as it didn't just happen in the weekly update. To be honest flatpak in Discover is a breeze after that palaver. It kind of got me into using Firefox in a hurry though.
Back then I often got Chrome needs to be updated warnings because I had forgotten to go search for updates. So @elliot13458 's comments rang a bell.
Like Discover or hate it, system defaults for Discover to check for updates is once a day, which means that if Chrome flatpak is updated then you will be told the same day it is out. That said I am still lurking around Solseek because I like simple(ish) code to do important things. I keep my own script to update software, firmware and flatpaks for when I want to see more of the workings or if there is a huge update like a fresh install.