I've written about aspects of this before over the years, but this is the first time I'm trying to put down a synthesis of those ideas. The upshot of my thesis is this: the irony at the heart of the Prophets' existence is that the ability to see all of time as simultaneous both grants them an omniscient perspective but at the same time traps them in an existence they have a frustratingly limited amount of control over.
Let's start by looking at time from two different perspectives.
From our linear perspective, time has a beginning, and an end. Events move according to cause and effect (let's put time travel and changing history aside for now). As we progress along the line, our past fades from view, becoming inaccessible and immutable. Our future, on the other hand, is unknowable and does not come into existence until we reach it. The only point of time on which we can exert any influence at all is the present, and that is only because it has the consequence of affecting the future.
From the Prophets' non-linear perspective, however, it's a very different story. For them, time is not a line but a point - a single moment where everything in the universe, including them, simultaneously comes into being and non-being. There is no past for them, no future, only an eternal present on which they can see everything and act on everything and nothing at the same time - because despite being able to act on the present, they cannot actually change anything because cause and effect are indistinguishable from each other, and also because they know what history is supposed to look like.
It may help to think of the entirety of history from the Prophets' perspective as a stained-glass window that comes into existence (from their point of view) all at the same time and which they can see and experience all at once, every moment, while from our linear point of view, each piece is assembled in sequence. We see only pieces of the window as it forms, while the Prophets can see its final form because for them it all happens in one moment.
This is what ultimately traps them, because they find themselves committed to the pattern that they know and see. One question that we often hear being asked is why the Prophets are so concerned with the Bajoran people? The answer, from this perspective, is simple: they are concerned because linear history says they did, and if they didn't, that would create a paradox that would disrupt their non-linear existence. So the actions they perform are according to the pattern they need to conform to in order to maintain that existence, namely the shape of the window/tapestry they perceive.
That form of the window (which we see as a goal being assembled whereas they already see it as complete) is not a goal, per se, inasmuch as it's what they have to make sure it is that way because it's meant to look that way. The ultimate benefit is not so much specifically the defeat of the pagh-wraiths, but simply because that making sure the final form is what it is will maintain the existence of the Prophets' history/timeline.
For the Prophets, everything is always happening right now, and they cannot depart from their predetermined actions any more than we can stop what's happening to us this specific nanosecond because from their perspective, the past - allowing them to anticipate the present moment and the moments to come - does not exist. And because their very existence is dependent on that single eternal present, they are helpless to do anything but follow what is already in the pattern, what has always been in the pattern. Any deviation from the way that pattern is supposed to be laid down causes them harm (that's what chroniton particles do - they create chronal disruptions), which could threaten their very existence.
To put it another way, the Prophets have to keep to the final shape of the window of history because that's the form that to them has already happened and has always happened. But we poor corporeal monkeys, not being able to see and therefore not bound to that pattern have the ability to change the pieces, or place the pieces in a different sequence, which annoys and terrifies the hell out of them. Annoys because we're not following the sequence which will lead to that finished form, terrifies because the picture in the end may not be consistent with what they know should be, or worse, the whole window could shatter.
So to try and get us to reach that final shape, they give us plans, hints, clues (the orbs, the visions, the emissaries) as to how these funny linear creatures should be building the window/timeline. "Put that piece there - no, there! - and that piece is next... no, not that piece, damn it, and no, you shouldn't even be using that piece!" And they can't tell us directly what to do because that action isn't in the pattern, and thus unavailable to them.
So when Sisko did his suicide run into the wormhole, he was deviating from the assembly instructions, sending the Prophets into an apoplectic fit and explaining their angry confrontation with him. So in the end, faced with losing a vital tool that will enable them to construct that final form versus having to change the shape or picture of it, they are forced to chose to go with Sisko's request, but warn him that the new picture that will be shaped is not going to be something he likes, and that's his punishment for not doing what he's told.
Now, this doesn't mean the Prophets don't have free will. It's that their "free will" is constrained by certain hard, almost insurmountable limits. Firstly, the completely free exercise of will in the same way as linear beings do requires the space and time to exercise it, and as far as the Prophets are concerned, there's no progression of time in which they can exercise the same kind of free will that we do.
It's similar to the concepts in the movie Arrival and "Story of Your Life", the short story it's based on. If understanding the alien language of Heptapod B expands your consciousness so you can perceive the future, does ensuring that it unfolds as you foresee it mean that your free will is abrogated? Or does knowing the future create an obligation that you should act precisely as you foresee it?
(There's also similarities to the differences between Elves and Men in Tolkien's Legendarium, where Elves are doomed to fate while Men are allowed to change their destinies... but that's practically another essay by itself)
From this perspective, the Prophets do have free will - they could very well choose not to act according to the pattern even though the pattern says they will act this way because they've always acted this way. But this is dangerous, as seeing the whole of their existence in this way creates an obligation to act just as the pattern says or else their reality runs the risk of collapsing, or changing into a form which makes them cease to exist.
So to sum up: the Prophets may seem omnipotent, and they have incredible powers, but they are still trapped by their very existence and perception of time.
I like thinking of it this way because it's both mind-blowing and ironic at the same time. Mind-blowing because it forces us to consider the perspective of a species who see everything in time in one single instant and raising the accompanying questions of free will and/or determinism. Ironic because for all the power the Prophets seem to have, they can only exercise it in this fashion.
In that sense, the so-called lesser, linear races have more agency than the gods because of the former's limited perspective, and that's just too delicious for words.