First off, I'm sorry this has happened to you. Not a good feeling knowing someone has been inside your house. For most people, the economic loss is secondary to the loss of sense of security.
I'm Canadian and live in Havana. Naturally, all my neighbours assume I'm a millionaire (I'm not, lol) but I am much better off than 95% of the population (there are wealthy Cubans aren't part of the "political elite"). This type of robbery is always on my mind.
Installing SD cards in cameras is probably the best suggestion considering power and alarms were disabled. Since no cameras were taken, the SD cards may provide valuable information (clothing, face capture, licence plate, etc). I've installed SD cards in my most important cameras (256GB, the largest the cameras will take) and make sure that they're good quality, brand name cards. Amazon is full of deals of garbage cards. Considering a 256GB card is a fraction of the price of a camera, it doesn't hurt to buy the best you can. My camera's would require a ladder to access. Fortunatley, they're set back enough from the street I still get 1000+ face captures a day off the two cameras running face detection.
For lighting, I use solar powered reflectors such as
these. They've easy to install, require no cabling to be run (other than between the solar panel and reflector) and, of course, stay on even if the power to the house is cut. I've seen them available up to 800 watts (requiring two largish panels which are incluced) which are about 30,000 lumens. They come on at dusk (when the panel stops being able to charge the internal battery the light comes on) and off when there's enough light to begin charging the battery. Only issue is they come with remote controls which seem to be universal between brands. It's a security issue but the IR receiver could be disconnected. This would render the remote useless but once you set up the light, there's really no reason to use the remote.
These reflectors have worked great and my original ones are going on two years. I should replace the batteries before they start to fail but this requires unmounting them (requires a ladder) and opening them to see exactly what kind of battery they use. I buy them in Mexico but they're available on AliExpress.
Back to face detection...two of my cameras run FD 24/7. They don't get all the faces at night (need to make some adjustments) but daytime is great. I have threads
here showing what my SD1A404XB gets. It's done 1000+ captures a day alone.
But ever day, I quickly review the FD captures. Just lets me see who has been passing (there's a few known thieves in my area) and how people have been looking at my property. While cameras are often used reactively to see how a robbery occurred, I use mine proactively to see who's been watching the property and the frequency in which people pass by. In the future, I'm going to run face recognition on a back-end to see frequency of the same faces. There's a lot of foot traffic in Cuba so this has been very helpful.
The same would apply to LPR in Western nations but that currently isn't an active concern of mine. That type of robbery has been, until now, VERY unusual. But, again, I will implement it in the future.
I also have a good relationship with the local police, particularly the "sector boss". He's been by to review footage a couple times and videos have solved two robberies in my immediately vicinity. Again, the thieves here work on foot so it's a bit easier.
Again, sorry this happened to you. But thank you for sharing. It's given myself, and others I'm sure, some excellent insight on how we can secure and "fortify" our homes and businesses.