Rear wheels need to be dished to account for the gears. The spoke calculators will give you different length spokes on opposite sides to account for the offset. I believe that reduces the differences in spoke tension on opposite sides.
Currently I have a single speed e-bike and a derailleur e-bike. Of the 4 wheels, the only one that doesn’t offset the rim from the hub is the one with the cassette. The hub is centered on that one because the cassette on the right balances the brake disk on the left.
For safety and handling, the front contact patch should be centered on the steering axis with the bike straight and level. One bike came from the factory with the front tire offset 5mm. The rim was centered on the hub, but the hub was offset.
The spokes were 250mm, going to nipples 25mm from each hub flange. Pythagoras said that meant the radial distance was 248.7mm.
Pythagoras also said that to change the axial spacing to 20 and 30mm, I needed to extend the spokes on one side 500 microns to 250.5mm and shorten the opposing spokes 500 microns to 249.5mm. One turn on a bicycle nipple is 454 microns. What a coincidence!
My spoke wrench is a 4” spanner that will catch a nipple on 3 corners. The length made it easy to loosen each spoke on one side exactly 1 turn, then tighten exacty 1 turn on the other side. When I finished, I didn’t need further adjustment. The rim had moved 5mm, it ran true, and the spokes sounded good.
For the lateral tensions to balance, spokes on one side would have needed 50% more tension than those on the other. The would be about 4 notes on a music scale, but they rang the same, as do the spokes on 3 other wheels with offset rims.
I grabbed the rim and tried to force it laterally toward the sides of the fork. It wouldn’t budge. If the tire was centered and true and had no lateral play, I considered the task complete.
I think that balancing lateral tension doesn’t matter with 13 and 12 gauge spokes because as long as they aren’t loose, they don’t have enough elastic stretch to let the rim move. An 18-gauge road bike spoke has about 25% of the cross section of a 12-gauge spoke. With greater elastic movement, they may require preloading (tensioning).
Sound tells me no spoke is loose, which could allow lateral rim movement, and none is much tighter than the others, which on a bump could lead to permanent deformation, I suppose.