There are different components to feeling weightless.
You can partially simulate weightlessness with neutral bouyancy in water. This makes gross physical activity feel like it would when weightless (well: weightless and immersed in a dense, viscous medium).
Furthermore, divers have great difficulty sensing "down" even when bouyant, so in that sense also they "feel" weightless (at least, they fail to feel their weight). Any form of support that's spread as evenly over the body as the force from an external fluid would feel about as weightless as that.
However, it's possible for a diver to have a sense of "down" from e.g. the inner ear or the organs. Humans shouldn't count on that to get to the surface in the dark, I don't know whether frogs can. An accelerometer in an air bubble in a box would of course work even if the overall gadget is neutrally bouyant. I believe that training underwater is not a good predictor of how dizzy/nauseous you'll feel in freefall, so clearly the feeling is different even if not obviously so. In some sense a highboard diver has more claim to feeling weightless than a deep sea diver -- aside from air resistance anyone falling does at least have uniform forces throughout their body.
Now, diamagnetic levitation is not a force from an external fluid, it's internal. With sufficiently even diamagnetic levitation you'll feel at least as weightless as you do when neutrally bouyant in water and possibly more so. So if you're happy to call that "feeling weightless", the frog would feel weightless in a flat magnetic field.
But aside from the shape of the magnetic field, the levitation will not be perfectly even, because your body is not universally diamagnetic: some parts are wetter than others, or perhaps more formally magnetic susceptibility need not be uniform throughout the materials of the body. So the question comes down tois whether the frog can detect the unevenness of the levitation. If not then it feels weightless. Probably the answer is like water for humans -- sometimes to some extent it's distinguishable from freefall, but the differencedirection of the weight is not immediately obvious.
Then again, if a particular frog is vomiting copiously in freefall but not in magnetic levitation it will tell you "sure, it feels very different". Vomiting feels different from not vomiting, regardless of how subtle was the effect on its ears that caused it to vomit!
What you feel in a harness is a force equal to your weight exerted on a few square inches that are not any of the usual few square inches "designed" for that purpose. So magnetic levitation would only feel like a harness if the levitation is primarily of a few small parts of the body, with much less or no force on the rest. I do not believe that this is generally the case, and those levitating frogs don't have their limbs dangling downward, but it's possible that it is.
So, you've got your theory and then you've got your messy practical details of the construction of strong magnets and of frogs. I suspect it really comes down to what the frog is trying to achieve, and what fine mechanisms frogs have that can detect "down".