I feel like some of the background or daily goings-on with the MC, like calling/interacting with family or friends outside the hotel, or lack of detailed info about his past comes down to two things.
The first is like you said, the MC is a vessel for the player to imagine themselves in and is left vague purposefully in order to better facilitate a sort of 'head canon'.
The second option is what I'd call episodic ambiguity/ the bathroom absence. Okay so what the heck is episodic ambiguity/ bathroom absence?... Well in most forms of storytelling, such as film or aduio or VNs, the authors leave out common daily details like using the restroom. They do this for a couple of reasons, one it's so common and universal to everyone that we simply don't need to witness it/ it's a bit gross to focus on and wouldn't add to the story. This is bathroom absence.
Then you have the idea of episodic ambiguity, which is the concept of events happening outside of what the viewer witnesses. Many television shows reference people, or places, or events that were never shown on screen. This creates the illusion of a larger more realistic and developed world, without having to spend extra time creating that scene.
For this VN the meta answer to your question about missing details in the MC's background comes down to the authors not having enough time and energy to create an infinite set of options, and their desire to create a blank slate for readers to project onto.
I my own in universe 'canon', I tend to write these oddities off as a form of episodic ambiguity and bathroom absence events.