How to reuse HLSL shader code?

They're called include files. In fact, by default all surface shaders in Unity use include files and you'll find most vert/frag shaders do too. Basically, create an empty text file and call it whatever you want. Then, change the file suffix/type to '.cginc'. Then, inside this file, you don't have to add any special information, you can literally just type the lines you want to be included. For example, if you wanted to reuse just a vertex function, you could simply have the following by itself in an include file (let's call it 'Resources.cginc');

 struct appdata
 {
     float4 vertex : POSITION;
 };
 
 struct v2f 
 {
     float4 pos : SV_POSITION;
 };
 
 v2f vert (appdata v)
 {
     v2f o;
     o.pos = mul (UNITY_MATRIX_MVP, v.vertex);
     return o;
 }

Then, in each of your shaders, at the beginning you just need to have the following;

 ...
 #pragma vertex vert
 
 #include "Resources.cginc"
 ...

And by default, the shader will use the vertex program from the include file we created, and therefore you don't even need to type it in this shader (so long as you initialise the vertex function pragma with the same name).