Any ideas on the best way to fill this gap?

I'm mid-way through my studio build. It's essentially a wood building that takes up 2/3 of the inside of a metal building, and the two do not touch except for sharing the same slab. The wood building has 2 doors, one in the main room that leads to the workshop area in the remaining 1/3 of the metal building and another in a vestibule that leads directly outside. In the latter case, there's a 1.75" - 2" gap (light blue in attached image) between the steel exterior door frame and the OSB on the outside of the wood wall. I want to fill this gap with something durable that won't transfer a lot of vibration between the two buildings. Some sort of black foam perhaps. I was hoping to get some ideas of what material that I could source online might work well. I was also considering how the material would be installed. My first thought is to put some L-shaped pieces (orange in the attached image) in on each side to prevent the material from pushing through and then just press-fit the material in (so, no adhesive needed). Any ideas would be very welcome. Thank you in advance. More details about the studio build here: https://studio.parscal.com

you don't really need a 2" gap. you can use a jamb extension on the inside wall to about 1/2" of the door jamb, then insert 3/4" semi-rigid insulation, and cover that with backer rod and flexible caulk.

Thank you for the reply! I like the idea of getting the gap small enough to use caulk. I'm thinking then I could use spray-foam and acoustic caulk with that design.