Microsoft project management software used to plan, manage, and communicate a project schedule and other information among workgroup members, project managers, and other stakeholders.
Rob --
The tool which you refer to as the Microsoft 365 online version is officially named Project for the Web. As it currently exists, you can IMPORT an MPP file from the Microsoft Project desktop INTO Project for the Web, but you cannot export a Project for the Web project to an MPP file for Microsoft Project. The closest you can come, and it takes a lot of work, is to export the Grid view to a Microsoft Excel workbook, and then copy and paste the relevant data from the Excel workbook into a Microsoft Project file. And when I say "lot of work", I have tested this, and it IS a lot of work. But I could encourage you to try this and see what your own experience is. Hope this helps.
It's a pity it wasn't clearer (IMO) that project web was knee capped by not being able to save mpp files or even sensible/adjustable pdf output format.
I have wasted time importing and editing what I assumed was an mpp file I could download.
So now I am getting Project client and take more unnecessary effort to recover from this mess.
Dataverse? What a pile of manure. How fundamental is it to be able to save a file.
Just like the British East India Company - hopefully one day MS will just collapse under the weight of its own hubris.