[Only a partial answer, more a collection of thoughts]
The 5200 is about the worst PPC Mac that has there been. While having a 603, it's crippled with a 32 bus interface and an 8 bit IDE. A straight guarantee for low performance. The 601 based 6100 is faster. So performance might be a rather limiting factor.
While the 5200 was first delivered with System 7, it might be a good idea to update to 9.1, much like it's suggested to use 8.1/8.5 on 68k Macs. 9.1 improves performance considerable over 7, as most code is native PPC, not being slowed down by emulation. In addition support for many interfaces got improvements, especially all around TCP/IP integration, quite related to your project.
Which brings the next important step, a modern Browser, but there is none. The most modern browse contemporary to Mac OS 9 is the Internet Explorer 5, stalling since 2000. Netscape 7 and Mozilla 1.3 are a bit more modern, but still way behind what the discord web interface requires. Classilla is essentially Mozilla 1.3 with development up to the mid 2000s and patches until some years ago. (I'm not sure about the state when iCab stopped development). As well not fit for the job. So no chance to run the discord web client soon.
The last resort would be a discord application, but the earliest I find requires Mac OS X at least. Being introduced in 2015 first, Discord is simply too new for any classic Mac. In fact, not even G3 board would help, as Discord only runs on 10.9 and later, so it's x86 only.
First introduction data of a software (here 2015) is always a good indicator what OS is required, as next to noone develops new mainstream (*1) applications for long gone systems.