Buildapc

By "control the PC" I assume you just mean power on/off. There's a few ways about this, some with additional hardware, and some can be done without any additional hardware.

• Wake On LAN (WOL) allows you to wake up your computer over the network. Easiest to implement if you have a smart home hub, but can be done without one. Some router admin pages have a tool for this. Doesn't usually work for shutting down, only waking. Doesn't require any additional hardware
• Wireless keyboard with a PC power button.
• Physical switch wired in place of (or in parallel with) the original PC power switch.
• USB home theater PC (HTPC or Windows Media Center) remote.
• Remote PC power button key fob. Sometimes comes with a PCIe card or some other device to install in your PC.
• Switchbot or similar IOT device that can be triggered remotely to physically press a button like your PC power button.

Any of these can be set up or modified in a way to be triggered by a bespoke button of pretty much any sort, provided basic electronics and soldering skills. Each has its own pros and cons. I'd look for "normally open momentary switches" or "NO momentary switches." One of the nicer switches people like to use for this sort of thing are called "anti-vandal switches."

Personally, I run Home Assistant on a Raspberry Pi at home, and I have a widget on my phone's home screen that triggers a Wake-On-LAN for my desktop PC so I can remote desktop from anywhere my phone has WiFi or cell service.