Not sure what you are asking?
Pushing a file means not live... and OBS Studio does not push files. OBS Studio can Record locally and/or it can livestream. People use OBS Studio primarily for livestream, but many of us do both, and some composite a Recording using OBS Studio, then use Video Editor for final tweaks, then upload file. That upload is typically done manually, via browser, as each content delivery network has its own process for accepting and tagging a new upload
So, if you want to Record a video, and later upload it to Restream, you'd use Restream's process for that upload (whatever that is).
Could you use OBS Studio to create the Recording? sure... all depends on what you are trying accomplish as to whether OBS Studio is the right tool for the task. Because of the computational power required for real-time video encoding, there are times when something like OBS Studio is the wrong thing to do... you'd be better off recording each camera input separately, then combining in a video editor... but it depends... and that can easily take a LOT more time (and end up with a better result)... so depends on expertise, budget, timelines, etc.