Legrande manufactures an under-cabinet track system for outlets and lighting called Adorne. It's expensive but should do what you want.

• Under-Cabinet Lighting & Power System
• Components

There's a free offer to help you lay out your system at the first link above. You can buy components on Amazon.

Legrande also makes Plugmold strips (example) which could be mounted under cabinets. However you'd have to handle the lighting separately, for example, with tape lights or fixtures (example).

Regarding the undercabinet lighting, make sure the recess for the lighting is toward the front of the upper cabinets, not the back. Installed toward the back you are lighting mostly the backsplash. Installed toward the front, the light is being shed onto the middle of the counter where it is most needed.

Regarding the outlets, I think you'll still need outlets in the backsplash. Will you be having a toaster or coffee maker or any counter appliance left plugged in? If so, you'd have unsightly dangling cords hanging from the outlet strips. IMHO, the better option is to install the outlets in the backsplash, but installed low and horizontally. That way they are hidden by the coffee maker, etc. You could also do a combo of the outlet strip and a couple outlets in the backsplash that you think will be necessary for coffee maker etc.

Also note that different regions have different building codes for the height of the outlets in the backsplash, and some regions have no code requirements pertaining to outlet height. In my area the rule is the outlet must be 4" from counter to center of the outlet, which when the outlet is horizontal, is a very nice height to be hidden by the appliances, but still able to get your hand in there easily to plug in. The bottom photo here is lower than that, so it depends what your locale allows.

Task Lighting Brand called Angled Plugmold. You can buy here on houzz or hardware resources. I use the APT series...it's slimmer but not a nightmare for electricians like some plug mold strips. They are tamper resistant like all outlets today...some people complain they can be hard to plug in.

I also like the lower regular outlet...no cords hanging down.