You can come close to the perspective with what we call a “normal” lens (50mm focal length on full frame, 35mm on APS-C Crop sensors).
The other issue you have is that human vision is not a sharp rectangle and that it’s extremely dynamic. You can look around a scene and refocus your vision almost instantly, while a photograph provides one fixed viewpoint and focus.
One more thing to improve perspective in images can be the use of comparisons in the image. A mountain with a house or a person at the bottom can look bigger because our brain knows how big those things are and understands the scale. In the case of the spider I usually photograph them next to a coin, as most people will recognise how big that is.