Valery, what about Bandicam, tried it?
The program has quite flexible setting of the quality of the recorded video. I have a video output of 300 mb for 10 minutes at 1920x1080 and 60 fps MP4 format. If you cut it to 30 fps and slightly reduce the video quality to 60%, then ~150-200mb will be released for 10 minutes.
With a reduced fps, the quality did not change much by eye, it was possible to lower the recording threshold even more to reduce the size.

In general, if you look for the optimal settings, you can pick something up. You can first try the shareware version, it has a 10-minute recording limit and will have a watermark, but you can make an opinion about the program.