After following ebastler's URL etc I no longer get the R/O problem.
This is what I see before opening any file

and this is what I see after loading one f3d file from the computer and clicking on the 3x3 icon

It all looks as I would expect.
Where does it say that? It is unclear to me how "the program" can be read-only, without reference to any file?
It doesn't say it anymore

But yes the program started up in R/O mode. So just a file viewer.
I think, contrary to my previous assumptions (which nobody argued with), there is more than one download URL for the "free" version of Fusion. And I was using a URL which produced the 30 day fully functional one, which then ended up as R/O and with all Save/Export options disabled. With the version I now have running, I never had a fully functional version (I judge that from the Export options, which are mostly grayed out, but STEP is available).
That said, I have not checked Ebastler's procedure with a completely new machine, email address and (yes you need that too, although it may give up eventually) mobile number

I am out of machines and definitely out of mobile numbers

Autodesk have set up a horrible "predatory" system, whereby they will make the program useless for anybody who ever has to open somebody else's f3d file, unless the user is on the same program version, which in the long run means the same OS version. They hacked it so that the f3d file cannot be opened by any older program version even if nothing in the f3d format has been changed. The smart way to do this would be to have a version # for the f3d file itself. Presumably this was done to control bootlegging, because it fairly quickly wipes out any patching of the executable, unless you use it purely for your own projects, in which case you never need to update it.