Scary moment, ignored right of way

I live in CH. I started driving car 2 Months ago. I am already 44 yo and have a lot of experience from bycicling and 45 kmh / 50 ccm scooter. Today i drove in the village i grew up. After a sharp turn follows a 500m straight.

After going around the curve i spotted a byciclist maybe 20 meters ahead. It was a racing bike and she drove around 30 - 35 km/h. I waited behind her and after 2 cars past the road was free for aeound 300m. I decided to overtake her with good distance, respecting her as much as i can. I went back in lane when she appeared in the side mirror. In front a crossing came up 50 m away. Traffic was slower there on my lane. The other lane was still free. I started slowing down slightly. In that moment the bike from before overtook me! I was slightly shocked(only for a split second) so now i had to slow down more. I commented to my wife about that bike driver. I was not very happy about her move given how stressful overtaking can be with little experience. I reached the crossing with around 35 km/h.

Then the car on the left lane suddenly accelerated and started crossing in my lane. I did an emergency brake and stopped 1m in front of his nose. It was my first emergency brake. I felt in control and wasn't emotional. My wife screamed. The other driver lifted his hand apologetically and backed up in his lane. I continued.

My wife was angry at me because according to her i slowed down to much because i commented on the bike, making the other driver think i let him pass.

Thank you for reading my story. What could i have done better. Should i just have stayed behind the bike at 35-40 km/h. Is that hindering of traffic if i can savely overtake according to art. 4 VRV?

Thank you for your feedback. Drive safe!