Inaccurate GPS track almost since I bought the watch in July 2019

GPS will have problems around buildings due to reflection of the signals from the satellites. What I experience and what I also see in your tracks is that close to buildings the track will push away from the building. A trick I use to get a track closer to buildings to actually move away from them.

I need really good tracks and often close to buildings since I'm using CityStrides to run all the streets in cities: https://citystrides.com/users/19643/map (all my running tracks in my home town)

I don't see any obvious issues in your tracks. Sometimes the track seems to be spot on and sometimes it drifts away and jumps around. It is hard in cities to get good tracks. You could test GPS soaking. After the green GPS signal you wait for about 2 minutes longer before you start your run.
https://support.garmin.com/en-US/?faq=xQvHXbfaT27Zr4hxZDvjv5

You got a 945 so look at the map before you start and make sure that you got a really good starting position. I always look at the map and wait until it got the correct position before I start.

Looking at your tracks, it looks very normal for a GPS watch, especially the FR945. You will not get much better by switching to another brand/model (you definitely can get a bit better, but in my opinion it's not a lot, https://www.dcrainmaker.com/2019/04/garmin-forerunner-945-multisport-watch-in-depth-review.html see GPS accuracy)

Near my home there're few buildings that are tall. But then around the river there's almost no buildings nearby. Except at the eastern side. I don't understand why in such an open area around the riber the track gets so messed up. Some days, it works good, but most of the times it's going back ad forth into the river.

My previous watch Suunto Ambit3 Peak never really suffered from this issue. And I used to run in the same area.

I run the exact same route (Invalidenfriedhof --> Spreeufer) 2-3x a week. My tracks aren't better. I have to disagree about the Spreeufer being an open area. On one side you have the water (reflections) and on the other side a wall/building/trees on both sides of the river. 

Near the Reichstag both sides have overhanging roofs.

I agree that the tracks are not as good as my old 920XT in most situations. Even if the track looks pretty bad, the distance is usually spot on for me. Until now I didn't have a watch with a good current pace, which is why I bought a Stryd.

I also pray they use a better GPS chip in the next generation to get back my old satellite fix time of the 920XT.

I have the exact same problems. My GPS tracks are just way off. And the fact that I've seen really good Forerunner 945 GPS tracks makes me wonder. Also bought my watch in July 2019.