Which psychological word describes this situation best?
Maybe you mean an engagement?
If though, a positive psychology have term flow state - when you fully immersed. Here is wiki article about it. Or hyperfocus - article.

Components of flow state:

Intense and focused concentration on the present moment

Merging of action and awareness

A loss of reflective self-consciousness

A sense of personal control or agency over the situation or activity

A distortion of temporal experience, one's subjective experience of time is altered

Experience of the activity as intrinsically rewarding, also referred to as autotelicexperience