Use ~/TorBrowser-Data/Browser as the browser data directory.

Index: xpcom/io/nsAppFileLocationProvider.cpp
--- xpcom/io/nsAppFileLocationProvider.cpp.orig
+++ xpcom/io/nsAppFileLocationProvider.cpp
@@ -335,6 +335,12 @@ nsresult nsAppFileLocationProvider::GetProductDirector
   if (NS_FAILED(rv)) {
     return rv;
   }
+# if defined(__OpenBSD__)
+  rv = localDir->AppendNative("TorBrowser-Data"_ns);
+  NS_ENSURE_SUCCESS(rv, rv);
+  rv = localDir->AppendNative("Browser"_ns);
+  NS_ENSURE_SUCCESS(rv, rv);
+# endif
 #else
 #  error dont_know_how_to_get_product_dir_on_your_platform
 #endif
