2-month-old Ragdoll sleeps a lot, looks low-energy but has appetite and formed stool; has dirt on it; suspect a cold

A cat with a cold shows runny nose, sneezing, eye/nose discharge, sleepiness, or low appetite, and these look like respiratory infection. So when such signs appear, first test for respiratory pathogens at a vet and rule out viral infections like feline herpesvirus or calicivirus before treating a cold.

Also, the black dirt on the cat is actually flea feces, meaning a parasitic infection rather than a cold. Do external deworming and related checks promptly, and disinfect the home and the cat’s belongings to stop eggs from surviving and re-infesting.