Nitrates are the the not-so-toxic part of the nitrogen cycle.
The decomposition of fish waste goes like this: Ammonia -> Nitrite -> Nitrate, with the two transitions needing a different bacteria.
Maybe the bacteria that decomposes Nitrite into Nitrate is not present in sufficient numbers in your aquarium. In this case you would observe a presence of Nitrites.
Maybe your Nitrates are all eaten up by some live plants if you have any. The other way to get rid of Nitrate is through water changes.
A reading of 0 Nitrate means either the tank is extremely clean, or completely without a functional cycle. Or maybe a tank without any live animals. If you want a cycle you need someone pooing in there. If you don't have build-up of the toxic ones, Nitrite and Ammonia, you should not worry too much.
Keep doing regular water changes they are very important anyway. You could do smaller, more often also, which is more safe. Never completely clean the substrate or the filter media.
Can you detail what are the "beneficial bacteria" that you add? I would recommend letting them make a population naturally.
2 weeks is also very young for a tank so it's possible the cycle is not yet stable. The 2 months old should definitely have something in it. If not Nitrate, then nitrite. If not nitrite, then ammonia should be present. Consider that your test-kit might be defective, try another one.
Bit of unasked-for advice: Betta would be a lot more happy, active and colorful in the 10 gal. Everything under 10 gal is extremely small, I would only approve it for shrimps or snails. Not even sure what's the point of a 3.5 lol.
Wish you to have fun with your aquariums !