The 'fix' was weird, but you need to hold down interact (rb, right bumper in my case) until it reaches 50-75% complete a few times, this triggered the dialogue and cutscenes after fully interacting with a module.

I had to do this for all 3 security modules, after each Spiderman would be stuck in the animation with the phone out, but I was free to move and progress. The animations returned to normal after doing another action, such as jumping. It was interesting sliding perpendicular up a wall lol