The hardware technology in your Silicon Dust HD HomeRun is the same as in the USB tuner cards and the PCI/PCIe equivalents. There are plenty of providers of software that can access this - and dont pay Hauppauge anything. Hauppauge isn’t some amazing company - they’re just a half-well-known brand in this space.
Hauppauge cards are just USB tuners connected to a PC; (even the Nova-T series are USB tv tuners interfaced over the PCI/PCIe bus, e.g. a PCI to USB adapter card, then a USB tuner card plugged into it - see Hauppauge WinTV-NOVA-T-500 - LinuxTVWiki).
You know what a HDHomeRun is? it’s a tuner interfaced run a small operating system and interface to the modulator and tuner itself and a network connection to send the TV signal out of… essentially the HDHomeRun is a little PC with a USB tuner or two, or four inside.
I’ve not looked into it, but these likely use a miniture version of Linux on an ARM chip interfacing to the “tuner cards” that are built in; and streaming the extracted programme over the network. The interface to the hardware is likely using LinuxTV for tuner interfacing https://www.linuxtv.org/ and other opensource components to strream the signal out onto the network
The firmware for most of these chips are available; many of the chips these days are software defined radio and require the firmware to make the chips work to understand dvb-t2, dvb-t, dvb-c, isdb, atsc, etc.
It is nothing to do with licensing.
Looking at the responses from others here, it is simply that the tuning features of the PMS are unloved and Plex rely on HDHomeRun as a working integration, rather than having to integrate and control the hardware more directly (with HDHomeRun it manages the hardware and you configure through a web-page).
Building a DVR is no small task; just look at the many lines of code is MythTV, TVHeadend, VDR, VBox and many others… Digital video recorder - Wikipedia so it is such a shame that Plex got so close and then “gave up” with supporting it… then again the world is moving to OTT streaming services