Try building a Windows manifest.

Makefile

@@ -14,6 +14,7 @@ ifeq ($(OS), Windows_NT)
 	PKG_CONFIG = $(MINGWBIN)/pkg-config
 	WX_CONFIG = /usr/bin/sh $(MINGWBIN)/wx-config --static=yes
 	PROTOC = $(MINGWBIN)/protoc
+	WINDRES = windres
 	LDFLAGS += \
 		-static
 	CXXFLAGS += \

extras/build.py

@@ -32,3 +32,13 @@ normalrule(
     commands=["iconutil -c icns -o {outs[0]} {ins[0]}"],
     label="ICONUTIL",
 )
+
+normalrule(
+    name="fluxengine_ico",
+    ins=["./icon.png"],
+    outs=["fluxengine.ico"],
+    commands=[
+        "convert {ins[0]} -resize 64x46 -define icon:auto-resize=64,48,32,16 {outs[0]}"
+    ],
+    label="MAKEICON",
+)

src/gui/build.py

@@ -14,6 +14,19 @@ WX_LDFLAGS := $(shell $(WX_CONFIG) --libs core base adv aui richtext)
 """
 )
 
+extrasrcs = []
+if config.windows:
+    extrasrcs += [
+        normalrule(
+            name="rc",
+            ins=["./windres.rc"],
+            outs=["rc.o"],
+            deps=["./manifest.xml", "extras+fluxengine_ico"],
+            commands=["$(WINDRES) {ins[0]} {outs[0]}"],
+            label="WINDRES",
+        )
+    ]
+
 cxxprogram(
     name="gui",
     srcs=[
@@ -35,7 +48,8 @@ cxxprogram(
         "./textviewerwindow.cc",
         "./visualisationcontrol.cc",
         "./layout.cpp",
-    ],
+    ]
+    + extrasrcs,
     cflags=["$(WX_CFLAGS)"],
     ldflags=["$(WX_LDFLAGS)"],
     deps=[

src/gui/manifest.xml

@@ -0,0 +1,13 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<assembly xmlns="urn:schemas-microsoft-com:asm.v1" manifestVersion="1.0"> 
+  <description>FluxEngine</description> 
+  <trustInfo xmlns="urn:schemas-microsoft-com:asm.v2">
+    <security>
+      <requestedPrivileges>
+        <requestedExecutionLevel
+          level="asInvoker"
+          uiAccess="false"/>
+        </requestedPrivileges>
+       </security>
+  </trustInfo>
+</assembly>

src/gui/windres.rc

@@ -0,0 +1,9 @@
+/* © 2023 David Given.
+ * FluxEngine is licensed under the MIT open source license. See the COPYING
+ * file in this distribution for the full text.
+ */
+
+#include "winuser.h"
+
+CREATEPROCESS_MANIFEST_RESOURCE_ID RT_MANIFEST "src/gui/manifest.xml"
+101 ICON DISCARDABLE ".obj/extras+fluxengine_ico/fluxengine.ico"