Though I have a Haibike with the Yamaha e bike drive system, here is a link to access what Bosch has on file with their drive and battery systems. Scroll down to Model Year 2015 for your application:
https://www.bosch-ebike.com/us/service/downloads/
Hopefully, other Haibike-Bosch owners could chime in and tell you how they check the battery performance.
Check around for speed tuning chips for your motor application to bring that speed up to Class 3 speeds. I installed a chip from the PearTune business on my Yamaha edrive. I would recommend starting with them first (link:
https://www.pear-control.com/) as they are very responsive and proactive to any questions you have regarding your bike; unlike others who might sell you a chip that can't be used on your application.
Be advised; I understand from reading around here that Bosch batteries are good for about 500 full charge cycles, then the performance drops off. Between having a 5 or even 6 year old battery (taking in the date your battery was made), the riding on it up to now and your desire to go at higher speeds then 20 mph, you might be on that edge where a new battery may soon be required. Just a heads up. Good luck, let us know how it works out.