According to this USGS pamphlet (last page, bottom right), solid green is "Forest". This link gives us
The mesomorphic tree canopy is typically >10% cover and often exceeds 5 m in height
(I was not able to find a good reference for a definition to "Shrubland" for the spotted irregular green to get a second notion of how green is used.)
In the map you ...
Vegetation is recorded
when it exceeds 20% cover of the landscape for an area greater than one acre
(0.4 ha), and 6 ft (2 m) or more in height - tall enough to conceal troops or
fugitives - with the same consideration for clearings within vegetated areas.
USGS Topographic Maps
Although @cbeleites' answer is quite exhaustive, I would like to add bikemap.net. I use it to plan my bike trips, I can connect dots on the map in any way I want, I can print the map with detailed frames, or send it to devices and use them directly from there. They have a lot of public routes added by other users, and if I see well, the most of the routes ...
As @Pont says, there are lots of train connections to Berlin, so one-way bike tour + return by train or also hopping from one nice region to another by train is definitively an option you should consider.
In terms of maps:
https://www.opencyclemap.org/ will show you that the whole place is full of bike routes, from small local ones to long distance trails....