Lower internet speed through router than internet speed from ISP

I have an internet connection of 500Mbps/100Mbps (tested through my PC using ethernet). For a project I'm working on, I decided to create a small LAN network using an old router which supports 5GHz 802.11n connection. I only have one ethernet wall port in my room though, so I removed it from my PC and connected it to the router instead. Then, I connected my PC to the router using another ethernet cable. When I tried running a speed test, the highest I could get was 93Mpbs/94Mbps. I also tested this through my phone using WIFI and got a lower result, so the issue isn't with the 2nd ethernet cable I'm using.

The router's bandwidth is also higher, I used iperf3 to check how fast the LAN connection over WIFI is and it was between 150-250Mbps.

How come only the internet speed is slow when the router is capable of much higher speeds?

Check the specs on your router.
This is perfectly consistent if the WAN/LAN ports of the router are limited to 100 Mbps. Which isn't unusual for a router that is a couple of years old.