Starlink system capability, at least for the most part, is limited by the aggregate capacity of the user beams, not the gateway beams. The user beams are indeed formed by a phased array (the gateway beams are not); the size/angle of each beam is almost exclusively a function of the number of elements in the array, which is almost exclusively a function of the physical size/area of the array. I'm not sure exactly where SX is right now, but I'd guess each sat can pretty much form a beam 'grid' with 5000 or so cells. So...the 350km sat can form the same 5000 (or whatever beams) in a much smaller area. It should be noted that what an increasing number of beams brings to the table is the ability to reuse spectrum more often within the total footprint of the satellite--that's the real technical enabler behind the increased density/capacity description from above.
The reason this doesn't math out is because capacity is first and foremost a function of regulated power on the ground. It doesn't matter if you have 1 or 100 satellites putting power down over an area; if beam size is the same and thus total number of beams in the area is the same, the max capacity (assuming the one sat is capable power-wise) is the same.
It certainly is true that a lower satellite with a smaller total coverage area results in the constellation needing more satellites to provide an equivalent level of coverage [to higher sats], I that's where you're thinking. Once that metric is satisfied however, more satellites can't actually add capacity. (More sats adds system upside in the form of redundancy, for things like dwindling energy budgets and failures)
