If you can avoid it, don't patch HDMI cables or HDMI extender category cables. Use pass-through plates for those. The fewer connections, the better, for HDMI.
If you want to use a rack mount solution for patches, you can get populated or unpopulated 19" rack mount panels, for binding posts.
You could install a flush-mount, recessed low voltage enclosure in the drywall, and use whatever you want to patch speaker cables inside that, e.g. terminal strips. Once the cables are patched, you would never really need to get into the enclosure again, so easy access isn't really necessary.
Terminal blocks (often rail mount) are another option for patching speaker cables, where the appearance isn't important (inside the enclosure), but they're generally pricey unless you buy used/ebay.
You can use Quickport/keystone Decora plates, or 19" rack-mount keystone plates, with the binding post inserts.
The more you dig, the more options you'll find.