But the blast that we see from Praxis is a two dimensional ‘disk’ which emanates outwards like the ripples in an ocean when a pebble is dropped in. these shockwaves moved only on a two dimensional plane, not a three dimensional one. The explosion only travelled along one axis, Surely if this burst of energy had hit a planet such as Qo’noS it would have caused even more apocalyptical destruction than we were told? The only explanation that I can think of is quite simply that the planet Qo’noS was just *slightly* below this two dimensional blast wave, therefore managing to avoid the brunt of the blast. The Klingon homeworld must have been hit by a ‘smaller’ blast.That would actually make things worse. If the mass blasts outward from the planet, then it will still have the same lateral orbital velocity. It'll still be in the same orbit, but with greater eccentricity, i.e. on a more elliptical path -- getting further out from the planet at apoapsis, but coming in closer to the planet at periapsis. So that would actually make the particles more likely to collide with the planet. (Imagine, say, pushing sideways on someone swinging on a swingset. It'll just make their swing more wobbly.)
The way to get something out of orbit entirely is to accelerate it forward. As it gains orbital velocity, it rises into a higher orbit, or leaves orbit entirely if it goes fast enough. But if you accelerate most of the moon's mass forward, then Newton's Third Law means that the big surviving chunk of Praxis will be decelerated and fall into a lower orbit. Which, again, could potentially make things far worse if it's decelerated enough for its orbit to decay.
It's highly implausible that a civilization at the Klingons' or Federation's level of advancement could artificially construct something massive enough to have a gravitational effect like that. Note how 80 years later in "Deja Q," the Enterprise struggled to move a much smaller asteroidal moon. (I suppose a Genesis device could potentially do it, given the magical abilities shown for it in TWOK, but Genesis was a political hot potato that was apparently outlawed, given how it was never referenced after TVH.)
Besides, the tide and weather patterns would eventually stabilize on their own once the mass of the moon debris settled into a ring around the planet. They'd be different from before, but they'd settle down over time. As with our current need to adapt to irreversible climate change, the goal would have to be to adjust to the new status quo, not try to recreate the old one.
It was the dilithium within the moon that exploded, so there's presumably none of it left. Although certainly the remains would be quite hot, so you could use it as a thermal energy source.
Picard season 1 seemed to indicate that they'd resettled on multiple worlds, and Discovery implied that they were essentially without a singular homeworld until they reconciled with the Vulcans and came together on Ni'Var (the planet formerly known as Vulcan).
I made a picture of how it happened in the film, but of course this is not to scale:

Speaking of scale, do we know how far exactly Praxis is from the Klingon homeworld? Praxis may not even be in a close orbit of the planet. Is it also possible that Praxis could have been a ‘Klingon moon’ orbiting another Klingon planet, or was it specified that it was a moon of the planet Qo’noS explicitly? A blast on the moon of a planet nearby to the Klingon homeworld of a scale as seen in Star Trek VI could still have resulted in damage to Qo’noS and it’s ecosystem, just like the blast damaged the Excelsior which was also *very* far away.