This straw-like growing medium was used to grow dhingri (oyster) mushroom. However, due to climate getting hotter here, the mushroom died, and now I am thinking if this medium is suitable for compost bin or better for mixing with soil to ammend? Or I need to just throw away this mulch like stuff?
Due to the long-straw nature of the fibres it will probably be hard to mix with other soil components so as far as that goes unless you can chop it smaller compost is a good idea; the rotting process will shorten the fibres and make them easier to mix up.
One use you might like to experiment with would be the same technique as using coir to grow salad leaf vegetables. The idea there is that the medium drains very well and allows roots to penetrate easily where they get lots of air. Since you are not growing the plants to maturity but just until they have enough leaf area that they can be cut for harvest, the problem of what happens when the plant grows big and starts demanding anchorage and nutrient variety never has a chance to occur.
If that works then cutting the leaves and immediately turning over the medium with salad roots intact would lead to a quick and efficient composting process.