Your parameters are quite demanding. The reference to the "chopsticks" being 0.05 mm apart is well beyond many FFF/FDM printers. A tolerance test model that I purchased from Makers Muse shows me that my printer can manage 0.40 mm separation but bonds together at 0.30 mm spacing. You're trying to get one-eighth of my best spacing on a filament type printer. I suspect your requirements would also be outside of many resin printers, as the x/y resolution is greater than your spacing.

Additionally, if you are using a 0.40 mm diameter nozzle, you will not get 0.20 mm line width. I've not seen a 0.10 mm diameter nozzle and I'll bet clogging would be a perpetual nightmare with such an item.

It's not out of the question that your slicer recognizes this impossibility and refuses to cooperate.

Wire EDM processes show up in my search as being capable of 3 to 5 microns (0.003 - 0.005 mm) and have prices in the tens of thousands and would work only if you can accept metal as your material. Graphite block EDM could also be used, but I'm not familiar with the steps necessary to create a grid of the provided description.

Additionally, photo-lithography and chemical erosion may be avenues to pursue.