Are gas giants supported by thermal pressure?
I am not sure what you mean by "thermal" pressure. Jupiter is supported by pressure, just like all objects that are in (approximate) hydrostatic equilibrium.

That pressure is provided by your everyday, temperature-dependent Maxwell-Boltzmann ideal gas pressure in the outer parts, but the free electrons in the interior become degenerate and so in these regions I suppose you would more accurately describe the pressure as being due to (partial) electron degeneracy pressure.

At the very centre there may be a liquid or even a solid core. In the metallic hydrogen model then this would still be degenerate electrons contributing the pressure. For a solid, rocky core, well solids are rather incompressible.

You can only describe Jupiter as being in approximate hydrostatic equlibrium. It is losing energy from its surface; this energy is supplied from gravitational potential energy and Jupiter is shrinking at a rate calculated to be about 2 cm per year. As it does so, the interior gas becomes denser and more and more degenerate and the pressure will become more independent of temperature. As a result, the rate of contraction will slow down and Jupiter will tend towards the radius of a "cold" body of that composition.