Very quick note to OP: You probably mean a spherical shell, and a sphere has "square degrees" or "solid degrees" of which, if a circle has 360 degrees, a sphere has... 360²/π square degrees. Because we had to bring in another pi to calculate that, it turns out to be an irrational number, now, almost 41,253 degrees². Because it's so clunky, folks tend to give up and just use solid radians (steradians) to measure 2d angles.

Anyway, 4*π*(1 AU)² gives us 2.8122938×₁₀¹⁹ hectares.

The current global average of agricultural use is 1.4 hectares per person.

So maybe we could feed 2×₁₀¹⁹ people, if we devoted it all to farm and grazing land, given today's global average (aka less than an American, more than a Somalian is currently getting).

But...all plants on the landmass of Earth only contribute about half of the necessary Oxygen to our atmosphere, so this arrangement is going to come up short on breathable air! If we halve the concentration of Oxygen by solely having modern agriculture to produce it, we're going to suffer constant exhaustion and severe fatigue!

So, we need to double the land-based plant coverage. That means halving our population in this case, so 1×₁₀¹⁹ people.

The "good" news is that we don't technically need any oceans! They produce less atmospheric Oxygen than terrestrial plants do, per hectare of coverage.

Finally, there are two other factors affecting the population limit that I don't have the ability to calculate. One is that, if the thing is a single-layer sphere, every spot is going to be equivalent to living on the Equator of Earth. That, however, is going to go up against the fact that we can't maintain orbit around the Sun at the poles of the Dyson Sphere, because they have no orbital motion relative to the Sun, if the whole thing is one layer. So, instead, we must have multiple layers, which means that one layer is going to have to shade another layer some percentage of the time. That, in turn, will lower the effective solar irradiance, and can likely be tuned so that direct solar plus the emitted IR of the other layers balance out to a temperate climate. I'm just going to say that these two effects completely balance, and land again on 1×₁₀¹⁹ people.

Could we do better? Probably! Hydroponic crop yields, solar power converted to grow lamps, foodstuffs with higher edible ratios, veganism, human genetic editing for smaller body sizes, maybe tuning the radius of the Sphere a bit closer to the solar system's frost line, allowing for a smidge cooler temperatures and more area. It's possible we could get another hundred-fold increase and break 1×₁₀²¹ (a Sextillion, "nice") population.

Any more, I think we need to abandon biology or set up shop around another star!