[Docs] Icon consistency. (#2895)

* Fix navbar brand (and work around annoying chromium bug).

https://issues.chromium.org/issues/41176872

* Update favicon to new logo.

* Update discord badges.

README.md

@@ -14,7 +14,7 @@
     <img src="https://dev.azure.com/discord-net/Discord.Net/_apis/build/status/discord-net.Discord.Net?branchName=dev" alt="Build Status">
   </a>
   <a href="https://discord.gg/dnet">
-    <img src="https://discord.com/api/guilds/848176216011046962/widget.png" alt="Discord">
+    <img src="https://img.shields.io/discord/848176216011046962?logo=discord&logoColor=white&label=discord&color=%235865F2" alt="Discord">
   </a>
 </p>
 Discord.Net is an unofficial .NET API Wrapper for the Discord API (https://discord.com).