The thing which determines how much space a video takes up is the codec that's used to encode the video, rather than the file format per se. Both mp4 and WebM are container file formats which support a range of video codecs.

The WebM format can use either the VP8, VP9, or AV1 video codecs. An mp4 can contain pretty much anything, but H.264, H.265 (HEVC) and AV1 are popular choices.

I would suspect that the key deciding factor for what codec Steam uses for recording is efficiency; you want the recording of video to impact the performance of the game as little as possible. So, you probably want to use a codec for which your GPU has dedicated hardware to accelerate the encoding.

For Nvidia GPUs, the onboard video encoding hardware (NVENC[en.wikipedia.org]) supports H.264, H.265 and AV1, depending on how new the GPU is, e.g. the GeForce RTX 40 series added support for AV1 encoding.

^ This not to mention there are more complex things than just the container and codec. Choosing the exact same codec and container can have significant different file sizes by adjusting things like the bitrate, fps, Colour range

Then there is compression efficiency vs compression speed. Compress more = compression takes longer to complete. Nothing stops Devs doing major compression for videos on store pages and in-game.

Recording and streaming at the same needs to balance compression quality and speed as if trying to compress too much requires more powerful hardware and the vast majority of users won't have the sort of hardware to do it quickly enough to do it on the fly. If you can't do it on the fly you need memory RAM or drive space to writing the data to so it can continue at a later time. Something I doubt a user will be wanting their CPU/GPU and Ram still busy encoding a video when they try to play a game