I spent six weeks in Europe 15 years ago out of a backpack. And to play the devils advocate…
Yes, you can do it all in one backpack - you’ll need to do some creative packing - bring a knit skirt for functions - and not mind wearing clothes a few days running and doing laundry. Don’t bother with anything that isn’t wash and wear - and if you can rinse it out in a sink, even better. Another option is to pack your backpack for your “travels” and ship back your suitcase after you finish your “stay”
(Don’t bring an iron. I overheard one girl say to another on the train “If I’d known I wouldn’t use the iron, I wouldn’t have brought it” - she had a full size iron she was hauling through Europe. She was also wearing tennis shoes, but had big ole combat boots tied to her backpack - try to get the pack to around 15-20 pounds)
Hit as many places as possible and get a flavor of as much of Europe as you can (this goes against everyone elses advice - which is good advice as well - this is just different advice). Sleep on the train, wake up in a new town, sleep on the train. Next time you go to Europe, you will have some idea of where you want to hunker down for a while.
I really enjoyed the day I spent in Paris (which surprised me - I am not a Francophile), loved Ireland and Wales. Enjoyed London, Bath and Glastonbury. Lucerne was stunning (but Switzerland was expensive). We were “stationed” out of an friends apartment near an army base near Heidleburg - which is a neat town. Trier in Germany is a neat place. We went to Copenhagen, which was pretty cool. I didn’t enjoy Italy and would go out of my way to avoid ever going there again (although we spent about two hours in Venice that I really enjoyed). We spent a day in Innsbruck eating torte…if you are eating Austrian pastries, its worth the trip.
Now, have I gotten back to Europe in the fifteen years since - no. (I might go to Ireland in a month or so on business - I’m actually trying to weasel my way out of the trip.)