APs don't "fight" (or more accurately: they always fight in a fair and standardized way, even in a single AP network). Medium access works the same between stations and APs on a different SSID (on the same frequency) as it does on a single AP/SSID.
It's a bit different on distinct but overlapping frequencies, since detecting a busy medium has to happen on the physical rather than the MAC layer, but if both APs are on the same frequency (and supporting the same maximum speed), the number of APs and SSIDs is mostly irrelevant.
This might change a bit when thinking about MU-MIMO, but I doubt that 2.4 GHz only IoT devices support that.