Apart from the main router you need to set them all up as access points. Such a string of routers all doing NAT and firewalling is the cause of your issue. You should also all use the same WiFi ssid name and password. This will allow your devices to automatically roam between them and you will have one flat network. Also make sure there are no Ethernet cable issues anywhere in this crazy linkage. This could also cause drops in speed or complete internet drops so make sure each link is connecting at gigabit speeds (the routers’ setup pages should tell you their link speeds). Much better would be to use actual access points and switches and a vlan aware router so you can do guest networks that are segregated but that takes a bit more advanced networking knowledge.

This really depends mostly on the capabilities of your devices. Just getting a better wifi access point/router combo won’t help if your devices can’t do any of it. Most devices are 2x2 MIMO and only support 80MHz wide channels on the 5GHz band. If you have a wifi 6 client (assuming you have a wifi6 router), the max signaling rate is 1200 Mbps, which translates to about 800 Mbps accounting for overhead. You can almost double this if you have devices that are capable of 160 MHz bandwidth but that is very rare, or if you have 3x3 MIMO capable devices (just as rare). Wifi 5 devices won’t get much better than the already quoted 500 Mbps. If you have wifi6e devices (just as rare) and a wifi6e wifi access point/router combo, you can also break the 1 GHz barrier. Wifi above 1 Gbps is still an expensive proposition.

What you priced out will work just fine. These are very good and the controller allows you to not have to subscribe to the cloud service. Any POE+ switch should work with these access points but if you don’t actually need 24 ports I would just get the same brand version and centrally manage.