(10.15.7) From where can the Quartz image filters be accessed?

I stumbled upon the Quartz image filters when I was building a Quick Action in Automator. From within Automator, I was able to preview the image filters, and some of them are actually pretty cool. I'm aware that the PDF Quartz filters can be applied via exporting an existing PDF opened in Preview, however this is not true of the image filters. Oddly enough, they aren't available in ColorSync Utility either, even though the PDF filters are. A few of them appear in Photo Booth. Beyond Automator workflows, is there anywhere else that these filters can be accessed?

Firstly, I think you mean Quartz Filters, not XQuartz. Quartz is the graphics subsystem in macOS, XQuartz is an X11 (unix GUI) environment for macOS ('X11 on quartz').

There are two types of Quartz Filters: 'Quartz Filters' and 'Quartz Composition Filters'.

Quartz Filters are normally found in /System/Library/Filters. They should be accessible in ColorSync Utility, under the Filters pane of the toolbar.

The following are the system installed filters in that folder:

Black & White.qfilter
Blue Tone.qfilter
Create Generic PDFX-3 Document.qfilter
Gray Tone.qfilter
Lightness Decrease.qfilter
Lightness Increase.qfilter
Reduce File Size.qfilter
Sepia Tone.qfilter

You may have other filters installed in either /Library/Filters or <user>/Library/Filters.

However, it's likely that you're talking about Quartz Composition Filters, which provide a range of manipulations to images. The Automator action to apply Quartz Composition Filters states:

This action can use any Quartz Composition of type Image Filter installed in the Quartz Composer Composition Repository (“/Library/Compositions” or “~/Library/Compositions”) as long as it does not depend on time.

The system-bundled filters are in /System/Library/Compositions. They include things like Blur, Mask, Mirror, and other effects.

As for where they can be accessed: the answer is 'not many places'. (Yet again Preview fails to be a flagship/showcase for the impressive features of the underlying architecture.)

You can of course create a droplet Application with Automator that will show the Action at runtime, allowing you to select and define the filter each time. (You may want to duplicate the image beforehand.)

These things are called Quartz Composition Filters because they were created in Quartz Composer, a developer tool for processing graphical data. However, this has been deprecated in Catalina, so it will not be developed further and may be removed from the OS at some later point.