### Godot version

v4.0.beta14.official

### System information

Windows 11 22H2

### Issue description

There's not much to it, simply noticed that if you have Find or Find+Replace opened in the Script Editor, the Multi-Caret functionality seems to stop working -- forcibly removing all other carets after the first character is typed. I'd expect the Multi-Caret to remain until unselected by clicking elsewhere.

The content of what's in "Find" doesn't matter, it happens regardless.

https://user-images.githubusercontent.com/8159582/214234069-cbcc1681-3f09-4b10-9a90-857cc91d41a7.mp4



### Steps to reproduce

1. Open the Find or Find+Replace tool in the Script Editor _(nothing has to be inputted)_
2. Add multiple mouse cursors with Ctrl+Alt+Click **OR** highlight something and then highlight additional duplicates with Ctrl+D _(or synonymous keyboard shortcuts depending on OS)_.
3. Start typing as if going to add or replace in all locations where the multi-caret is

### Minimal reproduction project

N/A
results_count = -1;
	results_count_to_current = -1;
	needs_to_count_results = true;
	search_current();
}
void FindReplaceBar::_editor_text_changed() {
	results_count = -1;
	results_count_to_current = -1;
	needs_to_count_results = true;
	if (is_visible_in_tree()) {
		preserve_cursor = true;
		search_current();
		preserve_cursor = false;
	}
}
void FindReplaceBar::_search_text_changed(const String &p_text) {
	results_count = -1;
	results_count_to_current = -1;
	needs_to_count_results = true;
	search_current();
}
void FindReplaceBar::_search_text_submitted(const String &p_text) {
	if (Input::get_singleton()->is_key_pressed(Key::SHIFT)) {
		search_prev();
	} else {
		search_next();
	}
}
void FindReplaceBar::_replace_text_submitted(const String &p_text) {