Why do you think the rim is worn out?
I see some wear on the brake track, but it is difficult to discern how much based on the photos.
Do you see some concave wear on the brake track? How deep? Something else?
It appears as if you have an odd paired 2-cross lacing pattern.
To reuse the spokes, you'll need to find a rim with the same ERD. You can either go by factory specs, or you can disassemble your wheel and measure it. Or, perhaps measure the nipple to nipple distance if you can discern the nipple length.
I think the paired lacing shortens the spokes slightly. With more even spoke distribution, you'll need a rim with slightly smaller ERD, I think, but I don't know how to calculate the difference. Perhaps figure out where the spokes would go if evenly distributed, and calculate the difference in distance to the bottom of the rim, or perhaps any representative point on the rim.
If the ERD is too short, you can toss in nipple washers to slightly increase the ERD.
Where do the current spokes end with respect to the end of the nipples. Ideally, when tight and true, the nipples should extend through the entire nipple & slot, and be flat with the bottom of the nipple.