Most electronic devices would not be substantially harmed by a geomagnetic solar storm similar to the Carrington Event. To understand why, it helps to understand how motors work.
The coils of a simple electric motor are made up of single, very long wires. That length is important because without it the electricity can't generate enough magnetism to turn the rotor. Even a small motor could have hundreds and hundreds of feet of wire.
What many people don't realize is that motors working in reverse are generators — and if you can apply electricity to get magnetism, you can apply magnetism to get electricity.
The Power Grid is At Risk
Which is why electrical power systems are vulnerable: all those transmission wires running for miles and miles. (long stretched-out wires are more susceptible than coiled wires, which is actually why phone and internet cable is twisted, but that's another story.) Bring a big old electromagnetic flux into play (which is what a geomagnetic solar storm produces) and you couple (electromagnetically) unfathomable amounts of electricity onto those wires.
To give you an example: while living in Texas my wife and I experienced a lightning strike about 1/4 mile (400m) away. The magnetic pulse that bolt of lightning produced coupled enough energy onto the wires of my house and the cables between my printer and computer to destroy my printer and ignite (I kid you not... ignite) the phone wires in my wall (a wire with too much electricity is a fuse by any other name).
Your cell phone, for example, and even your computer motherboards are generally not at risk. One or two may be lost due to the randomness of nature, but most would be damaged as secondary effects to the coupled electricity on the power grid.
So, your power grid needs substantial surge protection. The ability to shunt power to ground long before it reaches end-user locations. Most power grids actually have breakers and other protective devices in place for this very reason. Well, not to protect against a Carrington Event per se, but to protect against lightning strikes, the geomagnetics of sunspots, etc. But the biggest protection is foreknowledge. If we know in time what to expect, it's trivial to shut the grid down, ground it out, and let the power sink harmlessly into the planet. Check out this NASA article.
But, what about hard drives?
You have a colony world. Frankly, one hopes that you're still not using magnetic storage media as it's vulnerable to all kinds of problems in outer space. The issue of geomagnetic storms potentially erasing hard drives is serious enough to draw the attention of Bitcoin, which depends on predictable but temporary magnetic storage.
I would recommend that you advance beyond magnetic storage. Optical storage would be very difficult to disrupt via magnetism. Solid state storage that depends on affixing an electrical charge rather than a small magnetic field would also be more durable in this situation. Frankly, if you're using magnetic media you're probably toast because even a Faraday cage can't protect against the ground plane changing its value. (Faraday cages depend on the "ground" being at a predictably low potential compared to the item being protected. Start bouncing the ground plane around and you might as well have protected the device with a tarp.)
In fact, it's worth noting that a Faraday cage works on the very same principle as electrical grid transmission lines in a geomagnetic storm. The energy (whether emitted by something inside the cage or outside the cage) is coupled to the cage and shunted to ground. Same thing, slightly different math.
And the Satellites?
Well... You can't actually ground anything in space, so you do have a problem with satellites and space stations. Building them out of well insulated (or better yet, non-conducting) materials to protect inhabitants would help. Programming them to disconnect their batteries during the event would be nice... but how do you tell them to reconnect them? Off the top of my head, your best bet would be to position them on the far side of the planet in as low an orbit as possible to let the Earth's magnetosphere protect them as best it can. WB's physicists would know better if this would work, but if it doesn't, your satellites could be toast.
The problem is what the industry calls ESD - Electrostatic Discharge. A Geomagnetic storm can be thought of as that tiny spark from your finger that blows the $500 memory stick you just bought. Yeah, that spark is what we call ESD.
Chips are designed to do their level best to handle ESD, and elaborate designs on silicon are used to absorb and shunt the energy (I used to help design them). But remember what I said about my phone lines in Texas — a fuse by any other name. A Carrington Event makes that spark on your finger look a bit silly. But, we're talking about very short wires, and relatively very few of them. there really isn't that much that can accept the coupled energy. Consequently, the real problem may be where to put all the energy once it's be shunted around the electronics. It only has two places to go: the battery and the power generator (usually solar panels). Neither one is designed to handle a ton of energy.
So, your satellites, due to their probably inaccessibility, are at risk.
You don't need to go far out of your way to protect most electronic equipment from a geomagnetic storm. ESD protection in the chips will handle terrestrial problems because you can disconnect everything and have some buffering from the Earth's magnetosphere. Unplug all the wires. Roll up power and connecting cables so they aren't long lengths to minimize coupling. Make sure your building has proper grounding posts connected to your power system and throw all the breakers in your panels.
Your power grid must do the same thing. Disconnect and ground.
EDIT: Your power grid is completely protected if you bury it. This has other consequences. for one, it's a bazillion times more expensive to run power underground. For another, positive voltage underground causes corrosion. (Ideally you'd run negative power underground to avoid this problem — but now you're converting power polarity back and forth. Cost... cost... cost....) However, from the perspective of geomagnetics — bury it a good 6-10' and any solar storm that could affect the wires would destroy all life on the planet.
Your satellites might not survive. If they do, you'll need to probably replace all the batteries.
Finally, plan on cooking bratwurst over an open flame with the family and enjoy the most beautiful aurora borealis you'll ever see.
On the matter of mirrors... You appear to be thinking that the Carrington Event had at its core a threat of light. That's not really the case. Yes, there's light, but it won't do a think to any of the electronics. It's only the EMP (Electromagnetic Pulse) that's a threat to the electronics. The cost of putting any space-based planetary protection in place to basically make a "Faraday cage" for the planet is so great and so unrealistic that it's simply not believable. Worse, you'd need to shunt the power to the planet somehow, and tethering the shield would have its own problems. And it's massive overkill. Maybe for a planet like Asimov's Trantor, but not a new colony.
This isn't to say the light can't be a problem — it just won't be one for anything electronic. It very well could burn people to a crisp. Maybe you should cook those brats indoors....