As is the case with any other replay to video conversion, osr to mp4 conversion is not possible as well. OSR files from rhythm game osu! are not videos, just input data for the game uses to recreate the recorded rhymes.
The only way how to convert osr to mp4 or to achieve something similar, is to launch the replay using osu! and use one of the screen recording tools to produce a video from it.
In the past there were some converter apps that could automatize this task, such as Osr2Mp4, but it's not clear how many of these are still operational or supported.
Updated: January 18, 2024