If you had asked for a 3 or 4 cameras with 5mm lenses on 25x25mm base boards connected by MIPI ribbon cables under your collar to a few Raspberry Pis and a big battery in a backpack, you can do that today with off-the-shelf hardware for half your budget. They won't be synchronized, you can do that after the fact in your video editor. Getting someone to hold your hand and configure it for you will still cost the rest of your budget, but it's job done.
Or buy an off-the-shelf 360 degree action camera with included mounting pole and just use that.
Miniaturizing it into an ASIC and custom optics? That's man-years of effort and hundreds of thousands of dollars.
And both DARPA and the private sector have put millions to billions into miniaturizing and reducing power requirements for LIDAR into the baseball cap and it's still humanly impossible at the moment to fit it into the button of a baseball cap.
It's not even necessary to ask whether the pandemic makes these tasks a few percent cheaper. If you have an idea, get some basic information about the problem domain first.