Pychess (for whose devs playability against Fairy-Stockfish is primary condition to let new variant to be added) has Duck Chess (+- regular monthly tournaments) and Seirawan Chess (with House and 960 versions) which even has some popularity among players in lobby of that site.
I decided I would compare PyChess to Zillions-of-Games by conducting some games of Chess between them. After figuring out that the time controls in PyChess were per game rather than per move, I set them to the maximum and had Zillions-of-Games play at 1 second per move. With PyChess set to level 1, Zillions-of-Games won. With PyChess at level 8, it defeated Zillions-of-Games. To find out the lowest level at which PyChess can defeat Zillions-of-Games, I next tried it at level 4, and it lost to Zillions-of-Games. So, I increased its level to 6, and PyChess defeated Zillions-of-Games. Then I decreased it to level 5, and it defeated Zillions-of-Games again. So, level 5 was the lowest level at which I got it to defeat Zillions-of-Games with 1 second thinking time.
I then raised the thinking time for Zillions-of-Games to 2 seconds, and because PyChess had changed sides on me, I let Zillions-of-Games play White. While the previous game was very long, Zillions-of-Games quickly defeated PyChess at level 5. I then raised the thinking time of Zillions to 5 seconds per move, and it still lost to level 8. Then I raised it to 10 seconds per move, and it still lost to level 8. Not only was PyChess level 8 defeating Zillions-of-Games at these longer thinking times, but it was taking less time to move too, which is another indication of how strong an opponent it can be. While I could go further in comparing them, I am currently satisfied that PyChess can play well enough for it to fulfill the computerized opponent requirement.
Main point is that what you call Li should include more open source sites of this family, not only Lichess.
We currently have a Lichess tag for games on the Lichess website, which it looks like you have tagged the most pages with, and I was checking for that tag on the page. We also have a PyChess tag. I am not very familiar with Lichess or PyChess myself, as I was already busy working on Game Courier before they existed. So I have to rely on people like you who know more about them than I do to let us know more about them.
I decided I would compare PyChess to Zillions-of-Games by conducting some games of Chess between them. After figuring out that the time controls in PyChess were per game rather than per move, I set them to the maximum and had Zillions-of-Games play at 1 second per move. With PyChess set to level 1, Zillions-of-Games won. With PyChess at level 8, it defeated Zillions-of-Games. To find out the lowest level at which PyChess can defeat Zillions-of-Games, I next tried it at level 4, and it lost to Zillions-of-Games. So, I increased its level to 6, and PyChess defeated Zillions-of-Games. Then I decreased it to level 5, and it defeated Zillions-of-Games again. So, level 5 was the lowest level at which I got it to defeat Zillions-of-Games with 1 second thinking time.
I then raised the thinking time for Zillions-of-Games to 2 seconds, and because PyChess had changed sides on me, I let Zillions-of-Games play White. While the previous game was very long, Zillions-of-Games quickly defeated PyChess at level 5. I then raised the thinking time of Zillions to 5 seconds per move, and it still lost to level 8. Then I raised it to 10 seconds per move, and it still lost to level 8. Not only was PyChess level 8 defeating Zillions-of-Games at these longer thinking times, but it was taking less time to move too, which is another indication of how strong an opponent it can be. While I could go further in comparing them, I am currently satisfied that PyChess can play well enough for it to fulfill the computerized opponent requirement.
We currently have a Lichess tag for games on the Lichess website, which it looks like you have tagged the most pages with, and I was checking for that tag on the page. We also have a PyChess tag. I am not very familiar with Lichess or PyChess myself, as I was already busy working on Game Courier before they existed. So I have to rely on people like you who know more about them than I do to let us know more about them.