On a multilingual WPML site, your search and booking widget labels can appear in English instead of the site language. Check two separate things.
Text domains not scanned. In WPML String Translation, enable Theme and plugin localization scanning for the text domains homelocal and homerunner-toolkit. Most widget labels are translatable once those domains are scanned and translated.
Labels revert after interaction. If labels look translated on page load but revert to English after clicking or typing in the search widget, that is a known issue in the search widget itself. There is currently no workaround for this specific behavior.