Julie here from Shopify Support.
Generally, issues like these are theme-related and are caused by edits made to your theme's code. Installing new apps can also cause issues like these, as some apps may add code to your theme or interfere with other installed apps.
Have you recently installed any new apps, or made any edits to your theme's code? If your theme's code has been recently edited by either yourself or through an app installation, then you can always try rolling back to an older version of your theme. Doing so may restore the upload widget.
If not, then it definitely sounds like an issue with the Upload-Lift app. I understand that you've reached out to the Upload-Lift developers and I'm sorry to hear that they weren't able to offer any assistance. However, when it comes to getting help with third-party apps, the developers themselves are the best to assist. Since they know their apps' code inside and out, they should be able to determine what's caused the widget to disappear.
I recommend reaching out to them again to see if they are able to help you out with this. Otherwise, I suggest contacting a Shopify Expert who can examine your theme's code and help determine what's going on.
I hope this helps! I'm also curious to know if you've made any recent changes that could have caused the upload widget to disappear.