You could have shared mesh network, each (you, neighbor) with it's own vlan. You both win, great coverage and bandwith for both, and your AP's wouldn't fight (and cheaper too, since you need less overall AP's).
If talking is out, then you are only left with suboptimal options. Depending where you live mobile 5/4g might also be an option.
That's not how 802.11 medium access works: If two access points are on the same network, fairness should be identical in the "one AP, two VLANs" and the "two APs/SSIDs" cases.
On the other hand, if the issue is due to super slow legacy devices that just hog airtime, a single modern AP also won't help.
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.
Get an agreement with your neighbor.
You could have shared mesh network, each (you, neighbor) with it's own vlan. You both win, great coverage and bandwith for both, and your AP's wouldn't fight (and cheaper too, since you need less overall AP's).
If talking is out, then you are only left with suboptimal options. Depending where you live mobile 5/4g might also be an option.