ha ha you're lucky the two of the nicest and smartest ladies on the board are helping you out here! Just about everyone else wouldn't have been as nice or patient!
The Exo Terra is good for keeping a stable environment just be careful, they heat up really fast the ambient temperature heats up. Especially difficult in the summer. Right now it looks like your main issue is hydration and the exo Terra is good for that.
If it was me I would work to get her hydrated first of all. The fact that newspaper isn't soaking wet is a bad sign.
If it was me I would be spraying the tank for about 30 seconds to a minute with a good fine spray, as soon as all the leaves are dry do it again. The ground on the exo terra will pretty much never dry out on it's own, but it does need to be dried! When I switched to a screen I save a lot of money on paper towels!
Do not rely on that fogger as a source of drinking water, it is only to keep up the humidity and probably not necessary if you're misting correctly, but don't toss it just yet...
Eventually you will want to switch to a larger enclosure... is that the 18 x 18 x 24? Looks like it. That in my opinion is not big enough for an adult veiled plus once the laying bin goes in there goes all your space!
A 24 x 24 x 48 screen cage can be had for right around 120 usd (often less sometimes more) and would be well worth it to give your lady enough space. When / if you to get one then you might want to use that fogger.
Finally: It looks like you pulled branches from your yard or outside? If so did you sterilize them at all? Several here do not but I think it is a good idea especially in a glass exo terra where anything living in it is more likely to breed like crazy and not leave!
There are many ways to sterilize but i think boiling the wood for 20 minutes is the easiest, safest, and most effective effective for the effort.
I do like the aesthetic on your tank and I commend you for looking and spending time to try to give your girl a better life!
Thank you! and welcome! hope to see you and pictures of your girl around in the future.