A switch is a switch, It does not "split" signals, it "moves" packets between ports. High-end switches are more like routers.
What is the use case there?
If you move your router to the basement - where the modem will go?
If the modem stays where it is now, you'll need two cables - one for the WAN connection from the modem, and another one for the LAN connection(s) upstairs. There're hacks allowing one four-pair Ethernet cable to be split in two, but this will limit the speed to 100mbps.
For PoE APs, you'll need PoE switch (or injecto
All 4 ports share the combined speed back to your router. The cable between your router and the switch should be 1gbit. I doubt your AP combined can use that capacity. This assumes all traffic goes to the router.
Lets take a different example. You have a bunch of pc and a NAS hooked to the switch. You could have 1gbit of traffic going between the pc and the router. At the same time you could have 1gbit of traffic going to the NAS. In addition you could have files being transferred to between the pc.
A switch itself is never the bottleneck. A 4 port gigabit switch can send 1gbit and receiev 1gbit on all port all at the same time. It can pass a total of 8gbit of traffic at any time. Not that there is a realistic way to actually use all the ports that way.
Your bottleneck if you want to call it that is because you only have 1 cable to the router. I suspect your internet is not 1gbit but if this was really a limitation they do make switches and routers with 10gbit ports,