You can disassemble GameAssembly.dll with GHIDRA, IDA or any other disassembler that supports x86. Decompilation is also available but nowhere near as with dnSpy because code is not C# anymore. It is C++ and you will need GHIDRA or IDA Pro if you have it to get best code decompilation.
You cannot inject managed assemblies into the compiled GameAssembly.dll. But...
If game has moved on to IL2CPP you cannot simply edit the files anymore. You have 2 options to achieve your goal since you still have managed assemblies:
C# - Use BepInEx IL2CPP loader or similar and simply write a "plugin" (DLL written in C# code) which will execute in the game AppDomain and get you what you want. BepInEx comes with everything needed for a fast deployment and development since there are examples that will get you up and running in minutes. Use Reflection for maximum profit.
C++ - Reverse Engineer GameAssembly.dll.
Some tools to consider: IL2CppDumper for dumping the methods prototypes from GameAssembly.dll, IL2CppInspector to also dump but with some options on how you want it dumped. You can also make IDA\GHIDRA scripts to apply to GameAssembly database. And you could also look at Il2CppAssemblyUnhollower. Very important to learn how to cast some data types and such.
First option is much easier especially since you have access to old managed code (Assembly-CSharp.dll) and you can look up the source in dnspy.
Second option is a bit advanced and you will not get source code and you will have to use C++ and Read\Write into the process memory manually but as said but it is a good way to get familiar with IL2CPP because not every game\project will have managed assemblies for you to see the source code.