In this question, it's mentioned the Apple II's slot 7 was used by third party graphics cards. Is there any documentation on those? What were those cards and what were their capabilities?
There are two types of graphic cards that were produced back in the day:
- 80-column cards.
- Video enhancing graphics cards.
=== 80 Columns ===
For #1, there were a few companies that produced 80-column cards for the Apple II and II+ machines which were only capable of generating 40-column, uppercase-only text. Videx was one such company and produced cards that could generate 80-column and even 132-column displays, though this it is important to note that these cards only handled text mode - they had no effect on GR/HGR modes.
While this solved the issue of making the older II / II+ capable of displaying 80-column text, the problem was that the II's firmware only knew how to work with 40 columns. As such, it was left to the individual companies to come up with ways to do things such as clearing the screen or positioning the cursor without interfering with the Apple's normal operation. This led to incompatibilities and made it that programs needed to be specifically coded to support the cards otherwise unexpected results could occur.
Interesting to point out, these 80-column cards had separate video connectors for their output. I can't say I've seen all the cards ever produced, but I do recall that one would plug the Apple II's native composite output into the VideoTerm board which then had a separate line out which you would plug into your monitor. This was more of an automatic switch more than anything else as all screen contents were memory based and the card wasn't trying to decode the NTSC signal of the II.
To wrap up the topic on 80-column cards, be aware that the cards that went into the Apple //e's AUX slot were not graphics cards per-se, but simply RAM and firmware extensions to the machine. The ability to display 80-column text was always present on the //e's motherboard, but the card gave it the extra RAM needed for the higher density display.
=== Video Enhancing Cards ===
For #2, I'm assuming the spirit of your question was more around were there any cards that would have improved the Apple II's video capabilities beyond just displaying 80-columns or the standard GR/HGR modes. There was only one company that I was ever aware of that produced such a thing; Synetix's SuperSprite board. This was a board based on the TMS9918A video display processor which was effectively the same chip that was found in the ColecoVision, MSX, and TI-99/4 machines.
The SuperSprite board did plug into slot 7 to get access to some video signals that weren't in other slots. What it did was that it would overlay sprites on the Apple's hi-res screen. It didn't improve the underlying hi-res capabilities, but the end result was that you could get colorful, animated sprites with little-to-no load on the CPU.
Unfortunately, the board was not popular (probably due to it going for $395; about $1040 in 2020) and thus little-to-no software was ever produced for it.
=== Modern Solution ===
If we fast-forward to 2019, there is a product called the VidHD which is interesting and worth noting. While the purpose of the card is to simply add HDMI output capabilities to a slotted Apple II while maintaining complete compatibility with the machine, it also has an interesting side-benefit of being able to produce more advanced graphics modes for the older Apple II machines.
How this works is that the card operates by watching the bus and looking for accesses to the memory locations of the II that deal with video. When it observes something video related, it updates its own internal frame buffers which ultimately produce HDMI output. The trick here is that the card doesn't care whether it is being run on a ][+, unenhanced //e, or a IIgs - if it sees the right sequence of writes to specific memory locations, it is possible to trick it into displaying DHGR and even IIgs video modes on older machines.
That being said, since your question mentioned slot 7, it is worth pointing out that this card does not rely on the video signals in that slot and as such can run in any free slot (including Slot 3).
it's mentioned the Apple II's slot 7 was used by third party graphics cards.
I'm a bit suspicious here, as slot 7 wasn't any more capable for generic graphic cards than any other slot.
As Dirkt already mentioned in his answer:
[...] There's not really a lot you can do with them, except cater for some different TV encoding system.
And that's exactly the point about the additional signals (SYNC and COLOR REF). They support modification and transcoding of the existing video signal.
By default the Apple II delivers a (kind-of) NTSC compatible signal intended for direct feed to a NTSC compatible CRT/TV. If one wants to (or has to) use a different output standard (SECAM, PAL, RGB, etc.) the signal existing signal needs to be decoded and reencoded. To do so the card needs to be able to detect position within the video frame so the colour signal can be detected within the video signal - which is the third signal needed, provided by a pin header beside slot 7.
Of course this could as well be used to overlay the Apple II picture with additional elements, or use it as background for another video generator (like for a TMS9918). In any case the result had to stay within the same (TV like) capabilities of the Apple II signal.
A third use, light-pens, is as well based on the same effect of synchronisation.
What were those cards and what were their capabilities?
As mentioned, next to all were encoder for different video formats.
Having said that,there were of course alternative video cards, some with (for back then) extreme high resolutions like 512x384 in colour.