I have never heard of a lumpy sore throat!

But really, what they are saying is that, with this variant, many people are complaining of symptoms starting in their throat, however they want to personally describe it, if that makes sense. For some it’s scratchy, for others it’s a little sore, for some I guess it’s lumpy

, etc.
I don’t think it necessarily means that the home tests don’t work. It may just mean that there wasn’t enough of the virus detectable at the point the test was taken. Even with the PCR tests, people can be negative and then test positive. (We see that in the hospital all the time.) Once a virus enters the system, it duplicates over and over for several days until it reaches a level that it makes the person symptomatic (or not).
Someone in my life had a sore throat all week. Did home tests AND a PCR at the doctor’s office, all negative, and the doctor even said the chances of testing positive at that point were practically nil (when deciding whether to go to a family gathering). Was at a store yesterday where they had home tests so bought some and decided to test one more time. Grossly positive! That’s part of the tricky part of this virus. Even though tests can be negative, one may still be infected and able to transmit the virus before tests turn positive. I woke up with a scratchy throat today myself. Did a home test which was negative, but I have an appt for a PCR on Monday, too. This thing is everywhere right now. Taking precautions while I wait.