Flatpak writes files for installed applications with the full Flatpak (store) path. This patch makes it write just "flatpak", using Flatpak from PATH. This is similar to the NixOS [0] patch, updated for Flatpak 1.12.1

[0] https://github.com/NixOS/nixpkgs/blob/bf4167861d0f864b0fc457778d54feb4a2675ea2/pkgs/development/libraries/flatpak/use-flatpak-from-path.patch

diff --git a/common/flatpak-dir.c b/common/flatpak-dir.c
index 80ff5e5f..0c111c31 100644
--- a/common/flatpak-dir.c
+++ b/common/flatpak-dir.c
@@ -7134,8 +7134,7 @@ export_desktop_file (const char         *app,
         flatpak = FLATPAK_BINDIR "/flatpak";

       g_string_append_printf (new_exec,
-                              "%s run --branch=%s --arch=%s",
-                              flatpak,
+                              "flatpak run --branch=%s --arch=%s",
                               escaped_branch,
                               escaped_arch);

@@ -8467,8 +8466,8 @@ flatpak_dir_deploy (FlatpakDir          *self,
       if ((flatpak = g_getenv ("FLATPAK_BINARY")) == NULL)
         flatpak = FLATPAK_BINDIR "/flatpak";

-      bin_data = g_strdup_printf ("#!/bin/sh\nexec %s run --branch=%s --arch=%s %s \"$@\"\n",
-                                  flatpak, escaped_branch, escaped_arch, escaped_app);
+      bin_data = g_strdup_printf ("#!/bin/sh\nexec flatpak run --branch=%s --arch=%s %s \"$@\"\n",
+                                  escaped_branch, escaped_arch, escaped_app);
       if (!g_file_replace_contents (wrapper, bin_data, strlen (bin_data), NULL, FALSE,
                                     G_FILE_CREATE_REPLACE_DESTINATION, NULL, cancellable, error))
         return FALSE;