You are probably right. Logitech Craft is a nice looking wireless backlit keyboard and it lasts about 4-5 days.
Now Iām browsing Roccatās websiteā¦ dammit, this topic is gonna cost me money. 
Oh wow, those drivers are open source? That is actually really neat.
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If you want a backlit programmable keybaords that works on Linux the p3ker keybaords do just that. If your up for tinkering you can modify them to be wireless.
They are 60% keyboards though.
Okay I feel like I have been leading you around a little, and not really fairly.
There are very few full size wireless 100% mechanical keyboard, like count on one hand.
They are not programmable (by the way do you want the board fully programmable or just a few macros?)
They are almost certainly are not backlight.
There is the IKBC DC108 which is bluetooth and USB C, no backlight, not sure about programmable but donāt count on it, but does come with a switch to change it to QWERTY, DVORAK, COLEMAK and WORKMAN layouts.
The Filco Convertible 2, again not programmable and no backlight. http://www.keyboardco.com/blog/index.php/2014/12/filco-convertible-2-usb-bluetooth-keyboard-announced/
You will have more options for Wireless TKL boards, maybe even backlight ones or programmable, nothing on hand from me yet.
There are certainly many more again Wireless 60% keyboard with backlights and a few with programmability too as @Eden points out. but you are loosing ever more keys for features, not sure on your limit of either keys or features.
For the most part Reddits search function is absolute garbage so these are hard to filter down to something I can show you as I use them the most for odd boards but feel free to look into https://www.reddit.com/r/MechanicalKeyboards for all sorts of wonderous things, just not what you want exactly.
Now there may well be rubber dome/scissor switch wireless 100% keyboards with backlight but that is not my thing at all and I cannot help.
I am sorry to say you option are extremely limited with out some compromise, and potentially/very probably something you really want like wireless.
You very quickly get into the realm of making your own keyboard by hand to get what you want, and for the options listed that can be complicated.
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Well, thanks for the support and for putting in the time to do dig out info.
I guess I will have to stick to a wired one since there are some easy picks there, plus it doesnāt seem like thereās really a choice.
In my case I lose the 10keys for space, more room for my mouse, less distance for my hand to go from keyboard to mouse.
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Some of the apps I use make use of the numpad though.
https://www.reddit.com/r/MechanicalKeyboards/wiki/wireless-mechanical_keyboards
There is a list of wireless board to browse maybe there is something in there you have not considered. Sorry though, I have had this problem before.
I use razer and logitech stuff and rarely have problems.
All the talk of wireless keyboards, and back-lighting being a noticeable power drain ā does anyone designing wired keyboards try aim for power efficiency, or do they mostly not care as long as the USB spec can give them the needed power?
Could you notice the battery drain if using a laptop with more or less efficient wired keyboards?
The corsair ones have two USB plugs because there are USB2 ports that wonāt deliver enough juice.
Good gravy. Thatās kind of ridiculous.
If someone reading this is more looking for N-key rollover keyboards, Plover has a list on their GitHub page of keyboards people have tested:
Plover is cross platform, so some of those might not necessarily be Linux-supported, but since N-key rollover is something Iām personally interested in, thatās where I would start looking.
Not really, RGB means three LEDs per key, that is around 300 LEDs on a standard keyboard. Most light gets blocked somehow and even LEDs are not 100% efficient. So to get some light out of it you have to push quite a bit of energy in first.
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It certainly feels that way sometimes. For custom building and indeed In the majority if not all keyboards use a constantly scanning matrix waitingā¦ well sending pulses, hundreds a secknd, for you to complete some part of the circuit with a key press. Not sure how that bodes for electrical usage.
LEDsā¦ Are leds. They are basically as efficient as they get and they are certainly the highest power draw in a wired board. If they are addressable or even RGB that is yet another thing that takes processing that takes power so slightly worse again. The thing with leds is you can put a higher value resistor in and get much longer battery life for very little dimming, but there in is another problem. Any dimming of leds in a keyboard will be amplified by the layers it has to go through and much of the light being lost because it is blocked. You have to go through the switch housing or membrane and the cap, the cap being the main loss because they are usually frosted or milky white plastic diffusing the light. And there are other things like on MX style switches the light is only coming from one side directly with the switch mechanism itself blocking a lot of light. So for mechanicals the more light the better for visual purposes which is the point after all.
I know for wireless boards the wireless is what kills the battery, which would seem obvious. They do a lot to help in various way. Like sleeping g when not in use. Various revisions of Bluetooth like Bluetooth Low Energy (BLE). Other wireless options like their own dongles, not always good.
But at the end of the day the best way to combat this is a bigger battery. Which makes boards cost more and potentially harder to ship, people to not like shipping lithium batteries because of fire risk.