Berlin's craziest zick-zack bikeway was an adaministrative failure and erased after realization (my photo on Google Maps).
Funnywise rests of Berlin's oldest bikeways (from around 1900) are just around the corner (Claszeile, link to Google Maps). They are the dark sides of the street near the pavements. First bike maps with bike-friendly or bike-banned streets were available from 1888. A copy from on of early period (1898) can be viewed at the Center for Berlin Studies (ZLB) in Breite Straße 30-36. Electonic version searchable on https://www.voebb.de (search: Straubes Neuer Radfahrer-Plan; entry 2017; open URL at the bottom).
In Tech Museum you will find old bikes. The special exhibition “Gearing Up. More Cycling in the City!” is all about cycling in the city. From November 29, 2024 to September 7, 2025 in Ladestrasse.
Between 1950 and 1975 the bike traffic was declining 90%. Cars and advanced public transport were the reasons.
A revival started in West-Berlin in the 80s. A very good example you can still see in Klopstockstrasse which is anyway interesting for you with the buildings in Hansaviertel from Interbau 1957. I grew up there. I can tell you from this time that a Gropius building from the backside looks extremely ugly.
A special building from this car oriented time is the famous "Schlange" which is a building built over inner-city Autobahn.
Today Berlin's cycling network is approximately 2,376 kilometers long and covers the entire city of Berlin (source). This network size is very unique. Both inner and outer districts are included. The priority network is the centerpiece and has a length of around 871 kilometers. Very high quality standards apply to this network in accordance with the Mobility Act. Berlin is also working on "bike highways", official name Radschnellweg.
Other innovative solutions are intelligent lighting solutions, e. g. tested on bikelane Graefe- (Straße Hasenheide) and Boddin-Kiez (Columbiadamm).
More than for bike traffic Berlin is known for its relatively cheap and mighty public transport network. In 2023 it was voted as #1 best public transport system of the world (source). This green revolution started around 1850s and in 1904 as electrified version under today's high subway U1/U3 between Nollendorffplatz and Schlesisches Tor. Just as comparison: Copenhagen which is often named as green city started 98 years later with a subway. So, make a guess why they used more bikes, and have in the back of your head that for new cars Danish people pay a tax of around 70-90% of the price.
Finally: Berlin is a city in which mobility transition happens since over 150 years.