RenderTexture Painting - color blending issues

Unfortunately, your image doesn't seem like it uploaded properly in your reply (on that note, I'm not really sure why they're so finicky, but it's nothing new).

 // Attached to a camera
 using UnityEngine;

 public class BrushTest : $$anonymous$$onoBehaviour
 {
     public Texture2D brushImage;
     public $$anonymous$$aterial brush$$anonymous$$at;
     Vector2 drawOffset;
     Texture2D screenTex;
     RenderTexture rt;
 
     bool drawing = false;
     
     void Start()
     {
         drawOffset = new Vector2(brushImage.width, brushImage.height) * 0.5f;
         screenTex = new Texture2D(Screen.width, Screen.height);
         rt = new RenderTexture(Screen.width, Screen.height, 0, RenderTextureFormat.ARGB32, RenderTextureReadWrite.Linear);
     }
 
     private void Update()
     {
         if(Input.Get$$anonymous$$ouseButtonDown(0))
         {
             drawing = true;
         }
         else if(Input.Get$$anonymous$$ouseButtonUp(0))
         {
             drawing = false;
         }
     }
 
     private void OnRenderImage(RenderTexture source, RenderTexture destination)
     {
         RenderTexture activeRT = RenderTexture.active;
         RenderTexture.active = rt;
         if(drawing)
         {
             GL.Push$$anonymous$$atrix();
             GL.LoadPixel$$anonymous$$atrix(0, Screen.width, 0, Screen.height);
             Graphics.DrawTexture(new Rect(Input.mousePosition.x - drawOffset.x, Input.mousePosition.y - drawOffset.y, brushImage.width, brushImage.height), brushImage, brush$$anonymous$$at);
             GL.Pop$$anonymous$$atrix();
         }
         Graphics.Blit(rt, destination);
         RenderTexture.active = activeRT;
     }
 }

 Shader "Unlit/BrushBlend"
 {
     Properties
     {
         _$$anonymous$$ainTex ("Texture", 2D) = "white" {}
         _Color("Color", Color) = (1,1,1,1)
     }
     SubShader
     {
         Tags { "RenderType"="Opaque" }
 
         Pass
         {
             Blend SrcAlpha One$$anonymous$$inusSrcAlpha
             Cull Off
             ZWrite Off
 
             CGPROGRA$$anonymous$$
             #pragma vertex vert
             #pragma fragment frag
 
             #include "UnityCG.cginc"
 
             struct appdata
             {
                 float4 vertex : POSITION;
                 float2 uv : TEXCOORD0;
             };
 
             struct v2f
             {
                 float2 uv : TEXCOORD0;
                 float4 vertex : SV_POSITION;
             };
 
             sampler2D _$$anonymous$$ainTex;
             float4 _$$anonymous$$ainTex_ST;
             float4 _Color;
 
             v2f vert (appdata v)
             {
                 v2f o;
                 o.vertex = UnityObjectToClipPos(v.vertex);
                 o.uv = TRANSFOR$$anonymous$$_TEX(v.uv, _$$anonymous$$ainTex);
                 return o;
             }
 
             fixed4 frag (v2f i) : SV_Target
             {
                 fixed4 col = tex2D(_$$anonymous$$ainTex, i.uv);
                 return fixed4(_Color.rgb, col.a);
             }
             ENDCG
         }
     }
 }

^{(Ran out of characters in the previous comment)}

For my test, I attached the BrushTest script to my main camera, created a material using the shader and set that on the script, then used "Default-Particle" as my "brushImage" Texture2D value.

Of note, using Blend One One$$anonymous$$inusSrcAlpha with pre-multiplied alpha on the colors did have a similar-or-same visual output as Blend SrcAlpha One$$anonymous$$inusSrcAlpha without factoring in alpha, since the point of pre-multiplying *IS* related to influencing the final resulting value (I didn't exactly mean to sound quite so vehemently against the idea). I mainly draw attention to it because it could easily become misleading in how it relies on such a specific blending mode as well.

In the shader, I also set the color to have ~50% opacity.

That said, I wasn't able to reproduce the problem you're running into. Are there any other details you can provide that might make it stand out?

^{Edit: typo}