Yes that is certainly 1 possibility.

A scouting mission possibly.

Yes sadly the actual mission than the 4 explorers were on remains a bit of a mystery. Taylor makes contradictory statements in the film and even him and the others don't seem to know where they have landed. You don't attempt to colonise another world with only 4 people in a small spaceship with very limited supplies yet Taylor suggests that was their mission, so it still baffles me to this day why they were actually out there.

They were supposed to return to earth. The point the OP suggested
The astronauts was lied about going to another planet & it was simply return to Earth 2 study time dilation mission.

At what point of the movie did you see this plan exposed?

I recently saw it again. The plan was to land, study the planet stay a few years, f[% the hot blonde & RETURN 2 EARTH. They were never meant 2 stay there. Unfortunately the ship sank. So in as Taylor sed "we're STUCK here".

As previously stated, going to the Earth's future makes much more sense than four astronauts colonizing another planet.
Maybe it does but there is no evidence of that in the film.

There is no evidence of that. Taylor states at the beginning of the film that they were traveling to another star.
Taylor was talking to Nova in the lab saying something like 'Stewart was to be the new Eve with our hot and eager help." He definitely expected to go to another planet.
If you've seen 2001: Once the Discovery hit Jupiter's orbit, a video recording came on and explained why they were sent on the mission ( the monolith). The crew , Dave and Frank, didn't know why they were on the mission until then.
As previously stated, going to the Earth's future makes much more sense than four astronauts colonizing another planet. However, I don't have an answer as to why the astronauts wouldn't be told that.

I think the ship was programmed to go Earth's future.
There is no evidence of that. Taylor states at the beginning of the film that they were traveling to another star.
Towards the end , Dr. Zeus is tied up on the beach.
The character's name is Dr. Zaius.

True, I should've said "Maybe Zaius finally believed his story of arriving in a spaceship".

One of the purposes of Taylor's mission was to test Hasslein's theory of time dilation. We don't know if they were actually looking for another planet.
From both Taylor's and Landon's remarks it seems clear that they were looking for another planet.
maybe Zaius finally believed Taylor's story of traveling from the past?
Taylor never claimed he was from the past. He said he was from 'another planet in another solar system'.

One of the purposes of Taylor's mission was to test Hasslein's theory of time dilation. We don't know if they were actually looking for another planet.
When Zaius said he'd been awaiting the coming of someone like Taylor all his life tells me that stories of intelligent men hiding out in (or beyond) the Forbidden Zone had been passed down since the nuclear war. That may have been the original reason the desert was declared a forbidden area. And Zaius had always suspected one or more of them would find their way to the apes' community.
I've always believed that Zaius referred to Taylor's departing voyage as "his destiny" because he knew Taylor would find the ancient ruins showing that man had destroyed themselves in the distant past, and that it was his world the whole time (maybe Zaius finally believed Taylor's story of traveling from the past?).

I think the ship was programmed to go Earth's future.
After the ship sank, Landon wondered what happened, " We weren't supposed to land in water" Maybe an airstrip had been built for them for their return in 3978. but it got destroyed in the nuclear war and Dead Lake eventually formed on that spot. .
Towards the end , Dr. Zeus is tied up on the beach. "Yes I have always known about man . I knew of your coming and have dreaded it my entire life" "The Forbidden Zone was once a paradise . Your breed made a desert of it" So ancient apes, the Lawgiver, may have stumbled upon ruins indicating that Man had sent a ship that would be returning in the future. The knowledge that ascendants of the humans that destroyed the planet would return was entrusted to the Guardian of the Faith - Zeus.
Taylor makes a comment to the effect he has to find an answer to how apes could evolve from men. Zeus says, " Don't look for it , Taylor, you won't like what you find" As Taylor is galloping down the beach , Zira asks what he will find, Zeus answers "his destiny"
What was Taylor's destiny- to come back to his civilization in 2000 years. He did find his civilization farther down the beach.

How did the ship go off course and land back home?
Never answered in any of the films. Your guess is as good as mine.
Sending four people to another galaxy to colonize a planet doesn't make sense.
Very true. It doesn't make sense. But it seemed that Taylor was the only one who considered it a one way trip. And if the ship hadn't sunk, they would have had the option to leave the planet.