When you select Get data from a SharePoint list on this site option in quick charts web part, SharePoint retrieves lists from current site using below endpoint:
https://tenant.sharepoint.com/sites/SPConnect/_api/web/lists?$filter=(BaseTemplate ne 101) and (BaseTemplate ne 119) and (Hidden eq false)&$select=Id,Title,DefaultViewUrl
That means all the list types except Document library (101) & WebPageLibrary(119) and lists which are not hidden should be shown in List dropdown in quick charts web part.
Reference: ListTemplateType enumeration
Also, I have noticed that dropdown is showing only the lists which has at least one Number/Currency column.
The list should have at least one text and one number or currency type column, else the list will not appear in the dropdown list.