Sharepoint not refreshing on edit and submit a new form

You mentioned "..a gallery view with an Edit button" are you updating the record in Power Apps or the native SharePoint list form?

I suspect you may be using a Power App form since you mentioned a Gallery. If you are doing this in Power Apps I found you have to use the following in the Update Property for a Combo Box so it sends back to the SharePoint list the correct format since your data column is a Lookup Type. Meaning a Look Up type column must receive back the ID and the Title. You can replace "DataVardValue5" with what ever your data card name is on your form.

{

    '@odata.type': "#Microsoft.Azure.Connectors.SharePoint.SPListExpandedReference",

    Id: DataCardValue5.Selected.ID,

    Value: DataCardValue5.Selected.Title

}

View in Power App.

Hope this helps.