The subject matter of Sonnet 94 seems about as far from nature as you can get: a group of cold, calculating people who keep their true selves hidden behind a mask and try not to take everybody out when they wield their power. Given this topic, we wouldn't think that flowers would be the go-to metaphor to describe these powerful peeps, but Shakespeare pulls it off here. Sure, the poem's not about nature, but it finds some convenient thematic parallels in the natural world.
The "summer" in line 9 might represent either Nature itself or God.
The "summer" in line 9 doesn't represent anything, and that's just the point: the flower doesn't need the approval of anyone else to exist.