I have a Windows 2016 server that is running an php/mysql application on Apache (set up via XAMPP), and another application on Tomcat. I want to set up a static IP so that the php application can be reachable by any computer with the URL (not just computers on the same network). Would doing this screw up anything that might be using/referencing the IPv4 of the machine?
Go ahead, no crew up in such scenarios. Static IP is way more reliable than issued by DHCP IP in most cases. Actually you must have static IP address on the server if you want it accessible from outside of your local network. You can do that in two ways, either you would set static IP on network interface on the server or if your router supports static DHCP, then you can associate MAC address of server's network card to particular IP address you want for your server, so router will reserve this address and will always assign the same IP address to the server. Choose what is easier for you to manage. The only thing you need to keep in mind - is that by assigning static IP address doesn't guarantee you that it can be reachable outside of your local network. To make server reachable from internet, you need following:
Make sure that you opened on a server in advanced setting of firewall
(Control panel-> administrative settings -> Firewall) HTTP(s) ports.
Adjust you XAMPP setup to listen on all network interface (By default many such solutions listening only on the localhost)
The next step that need to be done - is to configure your gateway/firewall/router. You need to forward public port(s) 80 ( and 443 if you going to use HTTPS connections) to the server IP address on your local network.
If you don't have static public IP address then you need to use dynamic DNS 3rd party services. From this point your web server would be accessible by public IP address.
If you want your server would be accessible by recognizable domain name then you need to buy a domain and setup in the control panel of your registrar association (setup A record in DNS zone) between domain name and public IP address of where your server living.