You need to talk to HP tech support --- NOT the front line people (they know nothing about this problem and will give you the same unhelpful answers) --- you need to tell the front line people to escalate to someone who is knowledgeable about DCH drivers
and its associated UWP "hardware support app". You tell the front line people ANYONE knowledgeable to OTHER DCH drivers (doesn't matter if it is Intel, nVidia or Realtek) will be good enough to talk to.
Tell the tech support staff that you already read Intel's warning about catastrophic failures if DCH drivers are installed incorrectly and that Intel specifically warns about trying to roll back to legacy driver. And you understand that these warnings also
apply to the Synaptics DCH driver.
https://www.intel.ca/content/www/ca/en/support/articles/000031275/graphics-drivers.html
This is the most CONCISE and technically ACCURATE explanation you can give HP support staff:
You need to tell them that you originally had a legacy synaptics driver (that has a old style control panel dockable to the task bar), and Windows 10 automatically downloads and installs the new synaptics DCH driver (show the version number in the screenshot).
Then you ran Microsoft Store to download the "synaptics touchpad" app. The Microsoft Store originally said that you owned the app (show them the screenshot) and but then it turned to "error" (show them the screenshot).
Don't talk about anything else (like trying time lady's solution), it will only mess up the conversation.