6 years ago our cat was sick like yours and we brought it to the vet.
the initial blood test indicated serious things. they advised we put her down.
However we wanted to know what was wrong. they did the test for the next most likely thing-negative.
so we did another more expensive test for next most likely.-negative.
this went on for 2 more tests and a total of 3000 dollars so far-negative.
she had an autoimmine disease response but none of the actual diseases that usually cause it.
about 20 percent of cat's that get autoimmune disease and underlying cause is not found.
so with no definite cause we treated her with prednisolone for 2 months and her blood count returned to normal.
however she developed diabetes from this drug course( we were told this would likely happen).
6 years later our cat is still around. However it did cost us plenty of money. i figure at least 5 thousand from the initial incident and of course the constant lantus insulin and 2 shots a day.
my wife is very happy our cat is still around.
ironically we have now had Brinn for 15 years and she still hates me. Oh well.