Hi @Zwood,
What you need to do is add a visibility condition to the text or if you have a image also group them both and adding the condition to the group.
The condition will based on the all records>count. For example All Users > is equal to > 0 and a filter that property that you have added for search in the list so name > contains > input. Same filter that you added for the custom list.
See here : No Results Found for Custom Lists.mp4 - Google Drive
Adalo Docs : How to Create an Empty State - Adalo Resources
Edit : Just saw Archer’s post.
Thank you