This is L1d cache which is just 48kB for Ice Lake. We are also talking about context switches which are not happening very frequently. Applications that are generating load don't context switch all the time because they are busy doing work.
Then, when you context switch it is likely the context to which you are switching would like to use that cache for something. By the time we switch to your original thread it is very likely L1d has already been filled with something else.
I am pretty sure you would not notice anything except for very special, rare situations.