### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
#include "editor/plugins/debugger_editor_plugin.h"
#include "editor/plugins/dedicated_server_export_plugin.h"
#include "editor/plugins/editor_preview_plugins.h"
#include "editor/plugins/editor_resource_conversion_plugin.h"
#include "editor/plugins/gdextension_export_plugin.h"
#include "editor/plugins/material_editor_plugin.h"
#include "editor/plugins/mesh_library_editor_plugin.h"
#include "editor/plugins/node_3d_editor_plugin.h"
#include "editor/plugins/packed_scene_translation_parser_plugin.h"
#include "editor/plugins/root_motion_editor_plugin.h"
#include "editor/plugins/script_text_editor.h"
#include "editor/plugins/text_editor.h"
#include "editor/plugins/version_control_editor_plugin.h"
#include "editor/plugins/visual_shader_editor_plugin.h"
#include "editor/progress_dialog.h"
#include "editor/project_settings_editor.h"
#include "editor/register_exporters.h"
#include "editor/scene_tree_dock.h"
#include "editor/surface_upgrade_tool.h"
#include "editor/window_wrapper.h"
#include <stdio.h>
#include <stdlib.h>
EditorNode *EditorNode::singleton = nullptr;
static const String META_TEXT_TO_COPY = "text_to_copy";
static const String EDITOR_NODE_CONFIG_SECTION = "EditorNode";
void EditorNode::disambiguate_filenames(const Vector<String> p_full_paths, Vector<String> &r_filenames) {
	ERR_FAIL_COND_MSG(p_full_paths.size() != r_filenames.size(), vformat("disambiguate_filenames requires two string vectors of same length (%d != %d).", p_full_paths.size(), r_filenames.size()));
	
	
	Vector<RBSet<int>> index_sets;