Dispel the Bees
By some combination of solving clues, counting the number of clues in each section, and considering the title, we arrive at the conclusion that this is a puzzle themed around the New York Times' Spelling Bee. The answer to each crossword clue uses precisely 7 distinct letters and we can fill out a hexagonal grid radially outwards using these letter banks. For example, the answer to the first clue “Shape of this puzzle (7)” is HEXAGON, and its letters end up being filled in to the center 7 hexagons as follows:
A priori, there isn't a unique way to fill in the letters for each answer as they can be jumbled up. However, we can logically deduce how the letters are filled in based on adjacent answers. For example, the 6 answers at a distance of 1 from the center are CORN CHEX, EXCHANGE, GOT THE AXE, I GOT NEXT, OXYGEN TENT, and XENOSAGA. Each of these words contains an X and we use this to help us deduce that the X in HEXAGON is almost certainly going in the center of the grid. In such a fashion, we will be able to fill the grid uniquely, up to rotation and reflection:
Once the entire grid is filled, we notice that there are precisely 6 B's in the entire grid and they occur at the outermost 6 vertices of the hexagonal grid. The 6 bee images with dotted wings at the bottom of the puzzle suggest thinking of the two letters adjacent to the B's as a pair of "wings". This yields twelve letters which in cyclic order spell out JWST FULL NAME which clues the answer JAMES WEBB SPACE TELESCOPE, whose mirrors are befittingly in a similar hexagonal grid shape.
Appendix
The list of answers to the clues is as follows:
| Clue | Answer |
|---|---|
| Shape of this puzzle (7) | HEXAGON |
| General Mills cereal (4 4) | CORN CHEX |
| Act of trading goods (8) | EXCHANGE |
| Was fired, say (3 3 3) | GOT THE AXE |
| "After this, let me play" (1 3 4) | I GOT NEXT |
| Medical canopy to assist with breathing (6 4) | OXYGEN TENT |
| Monolith Soft game series (8) | XENOSAGA |
| Eye-catching (9-7) | ATTENTION GETTING |
| Orange pigment (8) | CAROTENE |
| Instrument company popularized by George Harrison (7) | GRETSCH |
| Not monotonous? (2 6) | IN STEREO |
| "Terrific", sarcastically (2 5) | OH GREAT |
| Greek drama trilogy (8) | ORESTEIA |
| Dips (7) | RANCHES |
| Economic downturn (9) | RECESSION |
| Stone often worn by Roman soldiers (5'1 3) | TIGER'S EYE |
| Nerfs and BBs (3 4) | TOY GUNS |
| High ___ (7) | TREASON |
| Squirts (8) | YOUNGINS |
| Diving helmet attachment (3 4) | AIR HOSE |
| Tile-placement board game (11) | CARCASSONNE |
| Deserving certain privileges (8 2) | ENTITLED TO |
| Drink whose logo includes a thunderbolt (8) | GATORADE |
| Statistic in chains and belts (4 5) | GEAR RATIO |
| Like Qatar vis-a-vis the FIFA World Cup (4 6) | HOST NATION |
| "The game is up!" (1'1 2 2 3) | I'M ON TO YOU |
| Game played with a stick and ball (8) | LACROSSE |
| ____ house (dwelling with no stairs) (3-5) | ONE STORY |
| Plant also known as cat's foot (9) | PUSSYTOES |
| Small and dingy place (7) | RATHOLE |
| Cinnamon candies (3 4) | RED HOTS |
| Schoolchild accessory (7) | SATCHEL |
| Exploratorium, for one (7 6) | SCIENCE MUSEUM |
| Racehorse of film (11) | SECRETARIAT |
| Mailed (4 7 2) | SENT LETTERS TO |
| Stuffed pasta (10) | TORTELLINI |
| Bastion successor (10) | TRANSISTOR |
| Agreement (10) | ACCORDANCE |
| Empire State Building style (3 4) | ART DECO |
| Whale cavities (9) | BLOWHOLES |
| Repress (6 2) | BOTTLE UP |
| Mandarin relative (10) | CLEMENTINE |
| The Doors drummer (8) | DENSMORE |
| It runs from corner to corner (8) | DIAGONAL |
| Suffice (2 3 3) | DO THE JOB |
| "mitmh2023", for one (6 4) | DOMAIN NAME |
| Lady Gaga lover (8) | FERNANDO |
| When you might see a pirate (9) | HALLOWEEN |
| Surfs (5 3) | HANGS TEN |
| Brand name towelettes used for cleaning (1 6) | J CLOTHS |
| Listlessness (7) | LANGUOR |
| Where you might find Poetic Justice (5 3) | MEDIA LAB |
| Small details (8) | MINUTIAE |
| What's left after deductions (3 7) | NET BALANCE |
| They might be found next to a crib (5 6) | NIGHT LIGHTS |
| Fresh ___ (3 3 4) | OFF THE BOAT |
| Vegetable cultivar used in sauces (4 6) | PLUM TOMATO |
| They often show up when right clicking (3-2 5) | POP-UP MENUS |
| Konami horror series (6 4) | SILENT HILL |
| ___ of Management (5 6) | SLOAN SCHOOL |
| Traitor (8) | TURNCOAT |