Can you turn your Mobile Phone into a HOTSPOT, connect the PS4 to the Phone via Wifi.
If this works, it proves the PS4 WIFI is working.
Also on your SH3 make the SSID for both 2.4GHz and 5GHz different, having the same name, this has fixed issues before.
Ie SSID and SSID_5G
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Red (VM SH2 AC Beta tester)
Running on 1Gbps VM service with SH4 in Modem Mode, with a ASUS RT-AC5300 router. With this setup I get Fantastic WIRED and WIRELESS Signals in my home. I dont work for VM. But I work in IT, and I know my tech.
My advice is at your own risk. If you are happy with my answers please press Kudo ?