Since the beginning of the last week I know, what was wrong. Handbrake was not fully supportet the power of the ARM Technolgy, especially the hardware-accelerated AV1 encoder. Now it does and the result is very nice.
A movie with 90 Minutes of Playtime will be now converted an MKV File in under 6 Minutes (1080p)
So if you are have a new Mac with ARM (M1, M2, M3), download the new Handbrake in Version 1.7.0 and enjoy the speed.
PS: To using the full coding speed, open from the Presets the Submenu "Hardware" and select "Apple Video Toolbox". You can select between Full HD an 4K.
There is also an Option in the Advanced Preferences where you can tick "Activate VideoToolbox Hardwaredecoder", but I did not recognized any boost in the other Presets of Handbrake. Not sure if this will be changed in a next Update.