Hi Khim Ba Hadur,
I go through your post carefully and as per your description, it seems issue happen to specific Excel file and get a “Read-only” message with edit permission.
I just tested from my side via live edit in SharePoint online with edit permission and I cannot edit Excel workbook. See image below for your reference:
As you mentioned “.xls file” did you change the format to Excel Workbook (*.xlsx)?
As you mention other test file they can edit, I think the problem could be related to your permission to this Excel file. If you don’t mind, could you please double confirm file permission with me? you can let the SharePoint site owner to check your account permission in this file. The site owner can right click on the Excel file in SharePoint and click Detail to open detail pane. In detail pane, click Manage access > Advanced to open the file permission windows > Click Check permission to find out your account permission of this file.
Make sure you account have “Edit” permission to this file so that your account can edit the file with edit permission.
To let us help you, could you please share a screenshot when you open shared Excel file with Edit permission.
I appreciate your patience and understanding.
Best Regards
Waqas Muhammad