The first thing that will happen is a domino effect as follows. You see a reasonably accurate telling of that in the first reactor scene in The China Syndrome, though in the movie the drama came from over-reliance on one indicator despite it being an outlier: a dumb mistake. Anyway,
- Generator trip. The main generator disconnects from the grid.
- Turbine trip. The turbine, with no load on it, would violently accelerate to destruction speeds, so steam is immediately shut off. This happens before any spike/surge damage could prevent it.
- Slamming the steam valves shut causes the flow of steam to immediately back up, spiking pressure and popping a pressure relief valve that dumps excess steam into a cooling pool. All this is contained routinely. This relief valve does not require power and will auto-shut when no longer needed. *
- most power reactors dump essentially all their output into the generator, so there's no other loads to sluff off extra steam onto. That means with the generator gone, they need to stop making steam ASAP or it will just keep popping the relief valve. So the reactor will either SCRAM, or do an equivalent sequence that has less paperwork and/or is more recoverable.
- The reactor has stopped fission. However about 20% of a reactor's heat comes from continued breakdown (decay) of the atoms that have already split. This continues, but rapidly tapers off to about 1% in an hour or so, and keeps tapering. This "decay heat" needs to be dealt with for months to come, but particularly in the first few days.
- Feedwater pumps, cooling water circulators, lighting in plant offices, battery charging etc. continue to run, to deal with this decay heat. They are run off external grid power. The station is now a drag on the power grid.
Now, a second thing happens: "station blackout". External grid power is lost. Emergency diesel generators spin up to power the normal post-SCRAM reactor cooling, essential station facilities, battery top-up, etc. They train for this. It's presumed that station blackout always happens alongside generator trip, since the grid is down. AFIAK it is impossible for a nuclear plant complex to use one reactor to power the rest of the isolated complex, but in a long term crisis, if you had a stable, well managed complex, engineers might find a way to do it.
Here is where you make a narrative fork in the road. Either your crisis affects the emergency diesel generators, or it does not.
If it does not, then the event is a big nothingburger as far as plant safety.
If the diesel generators are taken out, but they are able go over to the local CAT dealer or Sunrise Rentals and say "we need your biggest 4 generators, Right Now, by the way we are from the nuclear plant", and get them hooked in within 24 hours, again, nothingburger.
If they are not able to do that, then it becomes a chess game of skill and resources, against the clock. The needs will vary by peculiarities of that unit. For instance, Fukushima I units 1-4 are the same model of reactor. But all you needed was a fire truck to stabilize unit 1 indefinitely, because it had isolation condensers, as close to an "I win" button as you get in nuclear power**. However units 2 and 3 would be harder.
Restarting the power grid
Normally, restarting a power grid is am major pain because of all the load out there waiting to draw down any power you provide.
Only a few power plants can "black start", i.e. Start generating from a station-blackout condition. Nuclear power plants are defintely not on that list. Nor are big coal/gas thermal plants. All these types of thermal plants need to parasite tens of megawatts of power from the grid, to pump cooling (ultimate heat sink) water, boiler feedwater, fuel and combustion air.
Geothermal, same thing.
Windmills and solar don't have any parasitic draw to speak of from the grid. However they cannot blackstart for a different reason: by design, they need to "sync in" to the existing grid, and this is local to each windmill or solar panel inverter. Solar has no rotating mass, so solar is very stupid about staying in sync. Its inverters are designed to "follow the grid", a design philisophy which precludes any blackstart. Of course, that is software inside the inverter; a software update could tell an inverter "you are the one".
The "go-to" plants for blackstarting a grid are hydro. Their main generators also need to parasite external power for excitationof their main generators. However, better hydro plants are fitted with a small "donkey generator" which uses permanent magnets for excitation. This can deliver enough power to excite one of the main generators, allowing the hydro plant to "bootstrap". With its main generators turning, it can provide the station load necessary to start the thermal and nuke plants. The hydro plant can also, humiliatingly, use a diesel generator for this boostrapping, and even simply rent one down at the CAT dealer.
Blackstart capability could also be added to a thermal plant with a big enough generator and a smallish unit that can start off the generator and provide service power to the big units. Having blackstart ability adds a cost to the plant, so power grids contract with plants (pay them) to have the ability.
Rebuilding a power grid
Rebuilding a grid solves the problem of all the loads wanting to jump on at once. There are no loads, so you get to carefully manage who is reconnected.
Now you are talking about destruction of the power grid's wires and substations at a staggering scale. They have spares lying around, the narrative question is whether they are destroyed too. A transformer on a pallet would not be destroyed by EMP. They would have trouble manufacturing more on a large scale powering the plants with rental generators. So I suspect the power grid would get rebuilt chunks at a time, linking blackstart capable plants to other needed plants to manufacturing facilities able to make more wire and transformers.
Power grid wire is made of aluminum (the best conductor on earth that doesn't violently corrode near water, when you measure by weight, which is what the transmission towers need to hold up). Aluminum is everywhere, but takes a staggering amount of electricity to extract. Fortunately aluminum plants tend to be located near large hydro.
A narrative pivot point in your story is how the wires blew up; are they intact enough to use as "rope" to pull replacement wire (and if so, can they conduct electricity, since aluminum transmission line is uninsulated pure metal, a steel wire core with 1350 aluminum strands all around it). It's plausible for the aluminum to oxidize or burn; oxidation would leave the steel intact, which could conduct some electricity, an aluminum fire would melt the steel for sure.
* Unless it happens to be at Three Mile Island in 1978, and the indicator light is wired to show the actuator's position, not the valve's position.
** Which is why they gave so little attention to it, focusing on saving 2-3. Little did they know they had accidentally turned the isolation condenser off.