This question has so many layers to it. At the core, when people ask this question, there's at least some amount of anthropomorphizing going on. Are plants in any way equal to "people"? Do they have feelings like me? Can they be affected by pain the same way I am?
We tend to assume that the "people-ness" we often assign to dogs and cats, the consciousness of another mammal who looks at us from eyes like ours, who responds to kindness or cruelty in exactly the same ways we humans would, is a function of being more-like humans; and so things less-like humans must not have "people" qualities. It's sort of a survival skill; chopping into a tree with an axe would be much harder if you had a sense that it was screaming, every bite of potato a murder, every hazelnut consumed, the abortion of a hazelnut's offspring.
But what we're really doing is holding ourselves up as the standard to which all other organisms are compared, and that's objectively one of the most absurd things possible. Most organisms on Earth are bacteria. Compared to them, humans are absolutely terrible at reproduction and adaptation to changes in the environment. Within our own Kingdom, the animals, we're inferior to many organisms in many ways. We're out-massed by ants; if you took all the humans on Earth and put them all on one side of a balance-scale, and all the ants in the world on the other side, the ants outweigh the humans three times over. We have limited vision, smell, hearing, strength, speed, and endurance, and we take vast amounts of time to reach maturity, requiring decades of cultural input before we can even begin to function well enough to obtain a mate and produce offspring. We can't even produce light signals within our bodies, the way most animals on Earth do--most animals meaning all the creatures in the ocean who use light to communicate, camouflage themselves, frighten enemies, lure prey.
Can a tree feel pain from an axe? Can an injured or sick human emit chemicals that blow through the wind to tell other humans, far distant that there might be a threat to their survival? Will those chemically-signaled humans then pick up their weapons to fight, or get out their masks to protect against germs?
We have brains and neurons, and we are creatures who process dangerous attacks to our bodies using our nervous system. The responses that we have, we call "pain" and we also respond with hormone cascades and immune system activation. These are all chemical and electrical responses, at the base level they're entirely mechanical. "Emotion" and "feeling" are what we call those mechanical, chemical, electrical responses. What would a tree call all of that? As time goes by, the tree will begin to heal an axe-wound. When a boring insect chews up their inner bark, the tree could send chemical signals to other trees that there are destructive insects in the area.
We describe the experience in words and animal-actions. Trees would describe the experience in chemicals released, immune signals activated, bark regrowth stimulated, toxic chemicals manufactured. We can't really compare because we only know how to anthropomorphize, one direction. We can't seem to tree-morphize ourselves to work out what the experience might be like for the tree.
I know this all sounds philosophical instead of scientific, but that's also part of science--the validity of our observations is limited by our ability to eliminate our own biases. How long did it take scientists to accept the fact that trees "talk" to each other? Decades after the science had been laid down in a fairly solid way, because the scientists of the day were so firmly certain that trees couldn't communicate; no brains, no feelings, no "people-ness" that could possibly equate to the superior human experience. Their certainty prevented the larger scientific community from exploring that aspect of plant communication; decades of learning, delayed.
This is one of the best questions a curious human can ask, "Do plants feel pain?" The question can lead you to try to tree-morphize your viewpoint, instead of trying to anthropomorphize the tree. Some day, that might make you be the one person who can discover huge new insights in biology, thinking in a way that most humans are completely unable to contemplate.
