Just with regards to this part: > dessicants trap water in the molecular structure of the dessicant, so how do they extract it from the dessicant? The reason other water from air machines work is because they use refrigerant, and rely on condensation to extract water from the air. Because of this, they are very efficient, even in low moisture environments. Dessicants typically are far less efficient at extracting water.
There are many desiccant based dehumidifiers, they collect the moisture from the air and then use a heater to remove it from the desiccant (regenerating it in the process). The big advantage of these is they work at low temperatures, refrigerant based ones typically only work reasonably well above 15C whilst the desiccant ones work above 0C. Here's one on amazon for $200 ish: https://www.amazon.com/Ivation-Small-Area-Desiccant-Dehumidifier-Compact/dp/B07X43RGML/
I have a desiccant dehumidifier because my country is very wet but also pretty cold so in winter I can have quite low temperatures and want to keep my place dry. Winter bonus is it expels slightly warmer air. Maybe 3-4C hotter than intake.
Everything else you stated seems spot on, but just wanted to point out there are other types of dehumidifiers.
Get a rotary desiccant dehumidifier to dry the whole room:
https://www.amazon.com/dp/B07X43RGML/
Better and quieter than the compressor type