Do I have to start from scratch just to test the season theme? Level to 70 etc?
I think so - I believe that all your toons (even S19) will revert to NS on the PTR copy so you have to create a new one for S20 testing.
My guess is with the lackluster response about the season theme a lot of people are just testing the new sets with existing toons/paragons.
Yes you do. However, the PTR has buffs to help speed that along. You get a buff to XP making that faster, you get a buff to drop rates that is HUGE, so you gear up fast, and you have a PTR vendor selling the new items for Blood Shards. You will need to make a new Season char if you want to test the Season buff.
You can copy your Live account over to the PTR if you want to use existing blood shards to just quickly buy and test the new sets in Off Season. No leveling required unless, as you said, you want to test Season.
Also keep in mind, nothing you do on the PTR transfers back to Live, and the PTR can and often is, totally wiped even during a PTR test cycle. If they make a major change or bug fix, they often need to collect fresh data. That data is collected internally on their systems as we play.