This looks very much like Slater's Planet, a 1972 story by Harris Moore. There are several discrepancies though. Yet it looks unlikely to me that someone might have written a Slater's Planet's plagiarism (or vice versa).
- Exploration ship from Earth finds a nearly idyllic world - lots of beaches and water, compatible plants, etc.
Nope. The Arcturus finds a planet that appears to be wholly water - except for the one island. So yes, there are "lots of beaches and water"... there is also literally nothing else, except more water.
- When the exploration team lands, they unknowingly activate a sentient robot mind that is the real world. There are underground caverns and robotic arms hiding among the bushes and trees of the world.
Mostly check. The world is actually Beta, a machine world, obviously underground (well, actually underwater).
- The robot-world is camouflage for the robot mind running everything. It is actually a "caretaker" type robot mind, protecting an even greater robot-mind or its creators below in deeper caverns, or a shellworld around another world.
Check. Inside Beta, whose job is that of caretaker, there is Alpha, whose purpose is to fulfill its Primary Directive on behalf of its creators.
- The robotic mind tries to understand the "robots" that came to its world, including taking one or two "explorers" that wander away from the main group, transporting them down to the caverns, "disassembling" them, then being unable to "reassemble" and "activate" them, so it puts the pieces and liquids into a large glass jar and leaves it on the surface for the other "explorers" to find (and possibly reactivate? Obviously killing a human being and taking them apart will not let them be put back together again!).
Check for everything. This is exactly what happens to one unfortunate explorer from the Arcturus (except that the glass jar is carried to the other explorers by a robot, in the hope that they may be able to put the pieces together again).
- At some point the robotic mind is so afraid of being found out, it seriously considers awakening its secret, much bigger robot brain below in the lower caverns or inner world. There is something that will go wrong if the inner world is ever awakened.
Somewhat check. Beta wants to keep Alpha outside of the visitor's reach, but Alpha sees in the Arcturus a chance to fulfill its Primary Directive. Alpha and Beta are actually two parts of a single mind, that split itself in twain for better efficiency centuries before, with Beta being the caretaker or "unconscious" and Alpha the "thinker" (one side effect is that Alpha has no ordinary communication devices with which to make itself known to the Earthmen).
- The technology of the explorers is more 20th Century than 21st Century. The robotic caretaker does not use "quantum" terminology, so it comes across as being somewhat barely 21st Century technology as well.
Check. It is a 1972 novel after all.
In the end
Alpha develops a telepathic transmitter and contacts the Captain, offering him a deal - protection from Beta, who wants to dismantle the Arcturus to study its engines, in exchange for the Captain entering the inner world, reach Alpha, and pick up an object.
The Captain accepts and starts exploring the inner world, beset by Beta's mobile robots, while Beta tries to understand how they can orient themselves in its chaotic innards without any help from him or Alpha, as no detectable means of communications are employed.
In the end Beta realizes that Alpha must somehow be communicating with the humans, and its purposes are at odds with Beta's own, so the two computers fight. The Captain reaches Alpha, picks up what looks like a missile, the humans start upwards. Beta presses ever closer, but in so doing imperils the Primary Directive, thereby forcing Alpha to commit fully to a suicide attack. Both computers are destroyed and the Arcturus departs.
It is then revealed that the Primary Directive was to protect the "missile" and deploy it on a habitable world, where it will unfold into a self-replicating factory which will ultimately alieniform that world and populate it with the original planet's inhabitants.
They had no space travel and found this the only way to escape their world's destruction due to a cosmic catastrophe due in just weeks after the Arcturus's departure.
