The second prompt happens while playing the level, so there must be some secondary info saved. Not sure why I get the Cloud / Local Save prompt twice. This is similar to the behavior of unlocking an Xbox One achievement offline. After playing online for a while, the achievement unlocked.

I should also note that I got to 5 hearts while Offline. You can keep a Local Save on one machine at the end of a level, reuploading it the Cloud as needed. If you have 2 machines, you can use a variant of this without disconnecting Internet. (You may need to choose twice.) Go back to Step 1 and repeat until you get an upgrade. If you got shields, then choose Cloud Save. (You may need to choose twice.) Continue playing as usual until the next Shop. If you got an upgrade, then choose Local Save. See Step 7 for what to do if you get an upgrade or if you get shields. Play to the end of Level (multiple of 5), but don't exit the level. But as mentioned, even using this method, I seemed to only get Shields eventually. It's a shortcut to get to 5 million gold and (hopefully) get an upgrade at the Shop.

It has the added benefit of adding to your Total Gold Stats (but not what you have in your in-game counter). In my partial defense, it is difficult to get through 5 levels in the 40ish range when you don't have many upgrades. Eventually I got lazy, made too many mistakes, and was forced to restart. I would reload my Cloud save 4 times, yet always get Shields. But I seem to be stuck at 4 each of the Pickaxe, Dynamite, and Maps.

I was able to use that on my first playthrough to get up to 5 hearts.

And this is with a method to use the Cloud Save for backup. Do upgrades not start until a certain level? I started a new game, but I've only been offered Shields for the shops at Level 2, 6, 11, and 16.

Microsoft treasure hunt level 16