The tv series isn't really a reboot, as it doesn't really negate anything that came before. Battle for the Planet of the Apes already set up a premise of Apes as lords and masters of intelligent and talking humans and ends with human and ape studying under the Lawgiver, but a hint that things were on a delicate balance.
The recent Tales from the Forbidden Zone anthology book posited, in one story, that each future is one of several possible ones.
The tv series suffered from a "sameness" in episodes, as well as a much lower budget. There are some good episodes in there; but, most had the humans jumping out of trees on gorilla soldiers, hiding from Urko and his police, and winning over some ape or rescuing a human, or both. After a few weeks, it was pretty boring.
Logan's Run uses the same premise and repurposed some shots from the movie, in the pilot episode; but, took it a different route. Logan runs with Jessica, outside the city, and finds another world, with settlements of people who know nothing of the city. Francis is recruited by a council of elders, who live in secret and rule the city. They are all middle aged to senior and offer Francis a place on the council, if he brings down Logan, to keep the secret. Logan and Jessica discover a lab, with REM, and android (played by Donald Moffet), who travels with them. Francis still hunts them and they deal with other problems.
In both cases, they used the template of the original Fugitive tv series (with David Jansen), where he traveled from town to town, helping people in need, while avoiding the inspector hunting for him. The same plot structure was used throughout the 70s, for sci-fi series, including The Incredible Hulk, Planet of the Apes, Logan's Run, Otherworld, The Phoenix and some others.
Logan's Run was actually not bad, as DC Fontana, of Star Trek, was the story editor and had some good ones. However, the plot structure and low budget hampered things and you could only do so much.
Return to the POTA was the cartoon, from DePatie-Freleng, who produced the Pink Panther cartoons and were later purchased by Marvel Comics and renamed Marvel Animation. It was another timeline, and presented an Ape civilization that the original novel described, but was too costly to show, in the films and tv. The apes have technology, vehicles, tv and radio, and advanced weapons. Three humans land there, in the Forbidden Zone and have to leave behind their capsule. One, Judy, disappears. The two males meet up with humans and get caught when the apes capture a bunch. They are taken to the city and meet Cornelius and Zira, who help them escape, along with Nova. They eventually return to their capsule and reclaim some equipment and then discover the underground city and the mutants, which is where Judy is. They aid them, when lava is headed for their power generator (using a laser drill) and Judy returns with them. They eventually move the humans to a safer area and build Hopi pueblo buildings, in a cliff face, to defend against the apes. Along the way, they meet Brent, from Beneath the POTA, who knows Nova. In a later episode, they steal a P-40 Warhawk that the apes have rebuilt. They also help Cornelius hid a book showing apes in a zoo, in a monastery, high on a mountain (complete with an ape yeti).
From a story standpoint, the cartoon was really good; but, because of budget, they reused footage and the voice direction was rather flat. The character designs were done by Doug Wildey, creator of Jonny Quest. They also used a lot of dumb in-jokes, like a movie called The Apefather (this was the mid-1970s). Cornelius, Zira, Dr Zaius, Urko and Nova are all in the story. Urko was voiced by Henry Corden, who took over as Fred Flintstone, after Alan Reed died, and also voiced many villains in Thundarr and various Hanna-Barbera series. Austin Stoker, who appeared in Battle for the POTA, voiced one of the astronauts, while the female was voiced by Claudette Nevins, a character actress who appeared in tv and movies, including All the Marbles, as a female wrestling promoter (the film is about a women's pro wrestling tag-team, managed by Peter Falk)
The original novel had an astronaut land on a planet with an advanced ape civilization, where he was held for study, before escaping. When he returns to Earth, he finds that apes are now the dominant species. The original film modified this into what we know, then the Tim Burton POS tried to use the novel's twist, which fell flat (as did the whole movie, if you ask me).