Fuel burn is critical, which is why the idea is to mine/recycle/repurpose geostationary satellites in their geostationary orbit, leaving you with a geostationary space station, platform, super satellite, telescope, parts depot or whatever. The satellites aren't brought to Earth for recycling, but are instead recycled in place.
So once you get your Starship out to the geostationary graveyard orbit, where all the dead satellites are supposed to park, the only delta-v you need to expend is to move the satellites from their position in that orbit to a different position in that orbit - a collection point. That fuel cost is trivial and is dominated by how quickly you want to move satellites around. If the Starship is robotic, you could be very patient and move around at 100 km/hour (28 m/s) relative to the graveyard orbit velocity, taking 4 days to move 10,000km along that orbital path. It doesn't take that much fuel to bump a Starship by 28m/s.
Once you've got all your satellites at the collection point, you start in on disassembling, melting, degassing, whatever. The materials there are valuable only partly because they consist of gold, silicon, aluminum and so forth. Perhaps their greatest value is that they are already accelerated to geostationary orbit.
That amount of mass may be a rounding error by the time Starship gets fully in-gear. They may be lofting millions of tons of stuff a year, making the existing mass in geostationary orbit completely uninteresting. At that point, they may send up Starships just to bring that stuff back down so it can be put on display in various museums. Given the number of items, they may be donated to grade schools as curiosities.