I am sure there are many groups researching the mathematical
    properties of structures found in (living) nature (think patterns
    in fungi growth, selfoptimization of bone structure for weight and
    stability, paths in ant colonies or anything else in that
    fashion), but I just can't find any current projects in this
    field.

There is a yt channel for the Washington Philosophy Society. They have interesting talks by invited guests. You could then drill down into their published works.

Research papers are scored. The best get recognized by something like asters. You could look that way.