Deciding what route for Europe

Abit of an early one as this is for 2027 but me and the wife thinking of going Europe around mid to late August (roughly 20th August) and starting with a week and a half in Greece then going off to a few other countries. Totalling around 5 weeks were not sure (in alignment with the seasons too) if we should start in Greece then:

Go to Austria (for some hikes too)
Slovenia
Work our way from north to central Italy and end in Rome

Or vice versa (start in Rome and work our way up and end in Austria)
By the time we get to the last country it will be late September so I’m wondering if that’s going to be chilli for hikes in Austria if we end there.

Just wanting some opinions!
I wonder if we can sneak in south of France somewhere there too (we’re interested in visiting Nice)