The full solution is below, with a short explanation for each group. To avoid spoilers, play the puzzle or open the hints page before reading the answer panels.
BUTTER, YEAST, FLOUR, and SUGAR all fit the category "Baking staples". A bakery keeps these close. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Things in a gym
BENCH / MAT / ROPE / KETTLEBELL
BENCH, MAT, ROPE, and KETTLEBELL all fit the category "Things in a gym". Training rooms are their habitat. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Things that bloom
ALGAE / FIREWORK / ROSE / TULIP
ALGAE, FIREWORK, ROSE, and TULIP all fit the category "Things that bloom". Each can bloom in its own way. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Computer keys
SHIFT / ENTER / SPACE / ESCAPE
SHIFT, ENTER, SPACE, and ESCAPE all fit the category "Computer keys". They are labeled on many keyboards. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.