Great question! It sent me into a Google frenzy and here is what I found.

Q3 to me means three month period from 1st July to 30th September. During this time, there were 20 Starlink ‘V2 mini’ and 2 ‘V1.5’ launches. Each ‘V2 mini’ mission contained 21-23 satellites, which I averaged to 22, and ~50 in each ‘V1.5’ mission. Further, each ‘V1.5’ satellite weighs in at 306kg and each ‘V2 mini’ weighs in at 800kg.

Phew! With all that out of the way, putting all that together ((20×800×22)+(2×306×50)), we arrive at a figure of 382,600kg. Uncannily, this is almost exactly the same as the figure reported in the graphic, and of course there were a lot more Falcon 9 launches in the intervening period, leading me to believe the reported tonnage figure excludes Starlink satellites. See edit below.

This is all napkin maths done in the middle of the night, please feel free to (gently!) correct me if needed.

Inevitable correction: Q3 (as defined above) saw only one non-Starlink related Falcon 9 launch (source), therefore ~99.6% of reported tonnage was Starlink related!