Yes, Z590 motherboards support both Intel 10th gen and 11th gen processors.
This can be confirmed by checking the product page for a Z590 motherboard, which specifies “Supports 11th and 10th Gen Intel® Core™ / Pentium® Celeron® processors for LGA 1200 socket”.
The Intel Z590 chipset page also lists 10th gen processors under the “compatible products” section.
Considering Z590 is launching for 11th gen, new Z590 motherboards should not need a BIOS update for 10th gen support.
So to answer, does Z590 support Intel 10th gen CPUs? Yes!