Hello,
We have a recently reported issue with Experience Builder and offline maps, that the teams are working on fixing, that you might be running into. The issue is:
"Configuring the Search widget with a layer source from a map in ArcGIS Experience Builder creates field indexes with '-' in the name that will cause SQLite replicas to fail for the feature layer."
To check if this is the problem, you can look at the layers settings page in Online and in the Manage Indexes section view the Field Indexes. If you see an index name with a hyphen ('-'), this might be the issue you are seeing.