My young bearded Dragon

I have a young bearded dragon, probably around 4 months old or so. He was very active until recently. Recently he seems very sluggish, not a very big appetite at all and his right rear leg is not working. I give him baths in mild warm water daily and he seems to be pooping although not a lot. Could he be going through brumation? His color is good, and he spends most of the day basking in his log and isn't very active now. Any thoughts?

Beardies that young dont typically burmate, its most likely something wrong with husbandry and if not that then it could be parasites.

Whats the substrate/bedding?
How big is the tank?
What is the basking spot temp?
What is the cool side temp?
What insects are you feeding?
How many times a day are you feeding insects?
How many insects each feeding are you giving him?
How long have you had him?
Does he have any other heat sources?
Do you use a night time heat source?
What temp is it with that night time heat source and what temp is it without it?
What are you using to monitor temps?
What type of UVB does he have, tube, coil/compact (goes in a single dome), MVB (heat and uvb)
Is it a t5 or a t8? (uvb)
Is it a 5.0 or a 10.0? (uvb)|
What supplements are you using?
What type of greens is he getting for a salad (fruits and veggies too)

The leg issue is a bit concerning. Did he experience a recent fall or injury? And typically when a beardie that young stops eating like an insect bulldozer it means there’s a health issue or an issue with the husbandry. Parasites are one possibility (a herp vet can do a fecal test to see if coccidia or pinworms are an issue). Personally I would want to take my beardie to a vet if his leg wasn’t functioning, eating and lethargy issues aside. If parasites aren’t causing his lethargy and lack of appetite, then there’s a large chance the temperatures are off or there’s a UV issue. Are you using a Reptisun 10.0 UV tube? Coil UV bulbs are weak and essentially worthless, and over time can cause vision issues in reptiles. Is his basking temp between 100-110? And are you taking this temperature with a digital thermometer? Stick on thermometers are highly inaccurate so hopefully you’re not relying on one of these. Finally, is his substrate solid? If you’re using a loose substrate (sand, bark, walnut shells, etc.) there’s a chance he ingested some and became impacted, which can have very serious consequences. Impaction can also occur when a baby dragon is fed insects larger than the space between their eyes or insects with hard exoskeletons such as Mealworms. Without knowing anything about your setup, all I can do is say that these are the most common causes of the symptoms you’re describing. If you provide enclosure photos and specs on your UV light we can likely narrow it down.