Let me see if I've got the picture:

• You're renovating (walls are accessible now)
• Your walls are concrete (walls won't be easy to modify later)
• You're not sure what cables you need

Obvious solution: run conduit.

I’m using PoE Extractors to run some regular 12vdc stuff using existing ethernet cabling.

A couple of points to note:

• network switches won’t turn on power by default unless the receiving device asks for it using the right protocols, so you need to inject the power using the corresponding PoE injector at the other end of the cable. you can’t just snip the end off a RJ45 and wire it into things.
• Cat cable won’t take high currents, be sure to stick within the allowed range for the cable or it will melt and maybe bust your device
• there is a voltage drop over distance, be sure to calculate if you need to change your transformer as 12vdc could become 9 or lower by the time it gets to your device
• there are some really poor quality PoE injectors/extractors.
• running mains cable and having a transformer nearer the device might be simpler and cheaper in the long run.

I'm not sure I'm getting the gist of your questions, but as far as POE goes, if the device is designed to accept it, it will work at the negotiated PD voltage without problems, but you need a legit POE injector or switch.

If you're saying there is some "other" 12V power you're planning on running over different Cat6 cables, I don't understand why you'd want to do that.

Personally I'd run separate 12VDC cabling instead of pulling out from POE if it's simple to do, but if you get a splitter which will negotiate POE (assuming you don't run some older passive-POE setup) it should work just fine. But note, that POE goes up to 57VDC, so check that you can run your POE switch/injector with 12VDC at all.

Also remember that cables... are just cables. They will take whatever connector you put on thebend of it. So you can use a different one 12v so you dont accidentaly plug things in wrong.

But if you need to pull dc out of POE, you can get thigs that do just that. Search for POE extract or splitter. Many will let you pick wjat voltage to get out of it.

Imo youre better off running cat6 or 6a everywhere (better yet conduit where reasonable) and not running a 2 conductor pair along with your cat cable. Just terminate your cat cable as usb if you dont want to use an extractor.

Pull a bunch of fiber well you're running cables. Fiber is really cheap, it's expensive to terminate, but you can have the fiber pre-ran everywhere, and if you ever do need extra speed, or resistance against electrical interference, there you go you can borrow somebody's Terminator for a day

So a bit more thinking on this.

Looking at https://community.fs.com/article/understanding-poe-standards-and-poe-wattage.html POE could probably do a lot more than a few watts and could t feels like I could use POE to provide power for most of my devices providing cabled connection and power in one.

On the input side of things one idea I had was if I was running 12v DC on a separate cable run to power that I could have a battery / solar panel providing an independent supply since our 230v AC is strung from poles and does trip in bad weather.

Using POE does complicate that slightly I would have to find injectors that I could take that input and then extractors for USB, RJ45 and 12VDC output.

On the positive side of thing it would mean I could really reduce the number of 230 VAC sockets I would be putting around the house with just kitchen and laundry needing them.

Im also considering doing lightning at 12V LED rather than 230V