<wpml-config>
<elementor-widgets>
<widget name="search-form">
<fields>
<field type="Search form Placeholder" editor_type="LINE">placeholder</field>
<field type="Search form Button" editor_type="LINE">button_text</field>
</fields>
</widget>
</elementor-widgets>
</wpml-config>
in WPML >> Settings > Custom XML Configuration section.
2. Made a small change in the default language to reload the translation and now it shows the form button text in WPML Translation Editor for translation as you can see in the attached screenshot.