Pre and Post RS Germany tour

I would suggest spending extra time in Berlin after the tour - there's so much to see and experience in that city. You can get lots of tips and suggestions from the guide book and online and could easily spend several extra days there.

Snce it starts in Hamburg, I’d add at least a couple of days there or in nearby Lubeck ( or at least a day trip to Lubeck ). Most people on this and other forums recommend 4-5 days in Berlin. Do I would spend a 2-3 more days there after the tour

I agree about Berlin -- a lot more to see and do there than the tour could possibly cover. That's probably one reason why the tour ends there, to give you more time afterwards if you have it.

I haven't been to Dresden, and I see that the tour includes a stop and walking tour there, but if you want more of Dresden it seems pretty easy to return to from Berlin. If I'd had a couple more days in my Berlin trip I'd have gone to Dresden for an overnight.

We did the RS Germany tour in 2018 and added on days both before and after. Used trains to move between the locations.

Pre tour - Colmar (4 nights), Selestat (2 nights), Strausbourg (3 nights), Wurzburg (3 nights), Hamburg (1 extra night before tour).
We did one scheduled day tour "Four Wonders of the Alsace" an 8-hour minibus tour of local towns; otherwise we'd just wander around or take a bus to nearby towns.

Post tour - Berlin (3 extra nights after tour).
We did two scheduled tours - a day tour of Potsdam through "Original Berlin Walks" and a food tour "Berlin Food Crawl).

Enjoyed the extra time and sights. Time on our own allows us to decompress from the group togetherness of the RS tours. Other than booking the hotels, knowing the train schedules, and having the three day tours booked, we just took each day as it came, allowing us to pivot as needed for weather or laundry needs.

Definitely Berlin. We spent four days there in the Spring with 2 different guides including a day on our own to revisit some sites in detail. A lot of history and things to think about in that city.