There are 2 schools of thought about compression in Davinci:
1) Choose Automatic - Best and be happy with the results.
2) Render to an intermediate format and have an ffmpeg frontend compress to final size.
libx264 has far more settings than Davinci, so it can target quality or size more accurately.
As for the questions:
"Is there a recommendation how to calculate the value of kb/s?"
No. Bitrate is a function of how much you want to compress the material. See
(at 9:30) how a similar process.
Bitrate is useful when you have a limit: My XYZ second video must be under ABC MB.
To calculate it, it's (8000*ABC MB)/XYZ second = bitrate in kb. (small b for bit, large B for Byte)
To give an example, one of the worst to compress movies is called Kill The Encoder:
In 2160p it has a bitrate of 8000*1060MB / 111 seconds = 76435 kb/s.
https://en.wikipedia.org/wiki/Ultra_HD_Blu-ray specifies a maximum of 123 or 144 Mb/s in H.265. (984000kb/s or 1152000kb/s)
H.265 has a goal of being twice as efficient as H264, so therefore a maximum bitrate of 246 or 288 Mb (1968000 or 2304000 kb/s)
"Does it depend on timeline size (2K/4K) and/or the frame rate?"
Is 2K 2160p or 1080p? In either case yes. The larger the resolution, the more pixels, the more data is needed, the higher bitrate required. Same with number of frames. 1000kb/s for 30 frames/s is 1000/30 kb/frame, 1000 kb/s for 60 frames/s is 1000/60 kb/frame.
"What are the rules for calculating this?"
Get as high a bitrate as required for the quality required.
In a more practical world, the libx264 developers have created CRF, where you specify a quality (from 0 being visually identical to 51 being the worst possible) and let their heuristics deal with bitrate.
"It is not explained what the setting "Automatic" calculates."
The simple answer is: We don't know.
As a test, I compared a 2160p Mandelbrot to it's H.264 renders and compared the SSIM: Best is 98.79, 98.72, 98.53, 98.12 and Least is 91.55.
So in short, Best or High creates good enough video.
Davinci Resolve Studio 20 build 49, Windows 11, Ultra 7 265k, Nvidia 5070 TI, 576.80 Studio