Backpacking and canoeing I have generally gone with self inflating sleeping pads like Thermarest, shorty versions. But they do not fit well in a pannier, bike touring or kayaking I use air mattress that is more compact although it may weight more. My favorite air mattress is no longer made so I won't cite the brand and model, but there are lots of choices out there.
My most compact sleeping bag that is warm down to freezing temps is over 10 years old, a model no longer made. I also use a sleeping bag liner, it is nice to have on very warm evenings when a sleeping bag is too warm. And maybe an inflatable pillow. Bag is down, mummy style. I pack that with a thin stocking cap and down vest inside a compression sack that is rated for waterproofness. That gets packed in an Ortlieb, that is one thing where redundancy in waterproofness is not a bad idea. I do not recall the size I use, it is one of these.
https://www.granitegear.com/event-si...n-drysack.html
If you yank on a cord to compress the compression sack, you might tear a cord out. I put my stuff in the sack, then sit on it to compress it, then use the cords to take up the slack. That is just as effective a way to compress it, or maybe even more effective than just yanking on the cords. And sitting on it is much less likely to damage the compression system.
Tent weight and tent packed volume are nearly directly proportional. So, light tent will be a compact tent. Some people use a compression sack for these, but I find no problem in getting a tent packed down to very small size by folding and rolling it. Velcro strap around the tent to keep it rolled up.
My kitchen, below, excluding the fuel cannisters. (Yes, I read you are doing Esbit tablets, I am describing mine.)
From upper left to right, stove, some aluminum foil in a baggie, the white thing is a pasta strainer, measuring cut nests inside a titanium single wall mug that can also function as a tiny pot, bowl (green) nests inside large pot, the bottle inside that bowl is my instant coffee and that nests inside the insulated mug.
Lower left to right, a cheese wire slicer, silicone spatula, the white thing is a spatula that I think I will leave out in the future, folding fork and spoon, above the fork and spoon is an antique can opener, sheathed paring knife, cork screw, small windscreen (aluminum, folding, on top of the black storage bag, below that is a pot lifter, wooden spoon, on top of a coffee can plastic lid that is my cutting board, large titanium pot, upside down in ziplock bag is a fry pan, and lower right is the insulated mug that nests with my instant coffee bottle.
Not shown, some trips I bring the bottom two thirds of a plastic gallon jug to use as a bucket for hauling water, doing laundry, etc. Thin cord for a handle to hang it from. A bit over 2 liters in volume.
Not shown, bandana for hot pad.
Some of these things I am sure you would not bring, I suspect you have no need for a cork screw or cutting board, but that is part of my kit.
I do not have water treatment or filter stuff shown here, depending on where I go I bring something for that too.
I pack my tent with some other things that can get wet because my tent usually is damp in the morning. If you are packing a tent and stuff that has to stay dry in the same bag, think about how you will keep the moisture where you want it. When I am doing four panniers, the tent, sandals, some other stuff that can get wet are packed in the front right pannier. Air mattress goes iwith the tent, as the air mattress dries fast when wet.
I have never brought a folding chair on a bike trip, but I usually go where there are picnic tables. But I have seen some bikers carry them. I sometimes bring a piece of closed cell foam for a sit pad.
If you might do camp laundry, some light cord, roughly 8 to 10 meters and perhaps some clothespins may come in handy. But for only a week I suspect you will not bother with laundry in the campsite.
That is what comes to mind. I might add to this later.