I have a SecondSight VGA board and the developer's kit. It'll run at 1024x768. The engineering charter and purpose of the SecondSight board was to allow contemporary and sharper/crisper VGA monitors to be used with the Apple II. And it did this through interfacing a real PC-style VL-Bus videochip from OPTI / Oak Technologies. It was not intended to provide additional blitting or animation or a new programming environment. Though the capability was there by default in spades and droves. Too bad the demoscene never did anything with it. The manual which can be found here, lists 3 or 4 applications that would have made use of the special (but boringly standard) capabilities.
Then there's the SubLogic or Evans & Sutherland external graphics co-processor boxes - to which the Apple II would have been a controller. There is something like this for the TRS-80. And I reference it here because I can't find the E&S example, which may have been a myth? So.. The TRS-80 version has an Apple II tie-in of sorts. It's made to increase the resolution specifically. And only that. So that the use of the A2-3D1 animation libraries becomes practical. It's there to add "hi-resolution" to what is otherwise a very low-res display.
There's some DIY projects boards and the Arcade and Sprite boards. These are just that, based on the Texas Instruments chip. Their purpose was to create a new language and obviously add sprite capability. Among a small bump in resolution and/or variety of colors. the difference between the Sprite board and Arcade board was the former didn't have a sound chip and was cheaper.
A modern-day derivative of this is here:
Don't forget about the Apple II Video Overlay Card either. It was pretty adept at processing NTSC video and has 2 FPGAs on it in addition to a complete //e computer. It arrived rather late in the II series lifecycle and therefore nothing much was done with it.
It was interesting (and rather annoying) that some peripheral cards would need to "pick signals" from various points of the Apple II's circuit in order to do their job. Seeing as how that would be consumer unfriendly, the expansion card makers would incorporate a rather complete Apple II computer itself on-a-chip and just use the bus of your existing console. This was highly popular with accelerators from Applied Engineering, Titan, Saturn Systems, Zip Technologies, and others. The Overlay Card did the same thing.
If you look at the Apple II VGA adapter from A2Heaven, it does the opposite. It provides what is necessary to do the job. And you will need to use jumpers to pick several signals. Nothing wrong in that for today's classic computing enthusiasts. But in the late 80's and early 1990's there was a huge push to NOT do things like that. Plug and Play was on the horizon and hardware makers wanted to produce simple plug-in devices.
On the whole, custom hardware like this never really achieved widespread usage despite marketing's best efforts to make it all a simple plug-in board. The tedium and annoyances stemmed from limited processing power and nicher than niche software. The tedium lie in making that software work with the rest of the ecosphere.
There was simple the problem of combining the primitive with the sophisticated and not having enough raw power to blend it all together. It's like with the SecondSight board. Do you think the 1MHz Apple II bus could feed a native VESA LocalBus anywhere near capacity? I think not. In essence, the SecondSight board's SVGA chip could be considered off-board and part of the monitor itself - the way it was wired, the stark differences in technology. The usefulness and focus of the board lie in having the Apple II spit data at it as a second framebuffer, and that's it.