Explanation: you can draw a (family) tree by tracing paths from the circles to the bottom middle cell (the square root, if you will) to form the following words: SISTER, STEPBROTHER, BROTHER, MOTHER, GODMOTHER, GRANDMOTHER, FATHER, GODFATHER, GRANDFATHER, CARER.
Type of Twitter user that definitely isn't going to be a problem anymore, now that people can pay for a blue tick [edit: this feature became unavailable since this clue was written] [edit 2: Twitter may be gone soon]
7A
Droop
10A
Abbreviation for either an orchestra section, a narrow passage, or a variable type
11A
___ Geller, Israeli-British illusionist and self-proclaimed psychic
12A
US organisation that sticks to their guns (abbr.)
13A
American labour union leader [who, despite his surname, does not seem like a horrible guy]
16A
Word after red, ticker, or scotch
17A
See 40A
18A
Sash that, in modern times, doesn't actually keep a kimono closed (a series of ties known as koshihimo do instead)
20A
Because of
23A
Military branch with planes [no, not another name for a wing]
26A
Queens' water bearers? (abbr.)
27A
The practice of changing clocks twice a year, which may no longer take place in the US from 2024 (abbr.)
28A
Mauna ___ ("Long Mountain", in Hawaiian)
30A
Opportunities to break ties (abbr.)
31A
Notable elevator company
33A
Light white powder
35A
Measure of change of the size of something over time, such as a piece of vegetation or a collection of people
39A
Gary ______, American actor from 'Forrest Gump' and 'CSI: NY'
40A
Females who say 17A
41A
Late-blooming flower that resembles a daisy
42A
Shape that can be found by tracing paths (moving horizontally, vertically, or diagonally) from the circled letters to the middle cell on the bottom row
Down
1D
Two steps above corporal (abbr.)
2D
___ _ lot (gorged)
3D
Measurements for a person's figure, say
4D
Needle, or something targeted by a needle?
5D
That ubiquitous cookie
6D
Unlikely to make the first move
7D
Nickname for a dragonfly [although I don't believe they ever perform surgery on serpents…]
8D
Prince Valiant's son, in comic books [it's just 12A backwards]
9D
Part of LGBTQ+
14D
____ McEntire, American singer known as "The Queen of Country"
15D
Sufficient, informally [or in a text, if you really had to save letters]
19D
Not online (abbr.)
21D
ACME explosive purchased by Wile E. Coyote
22D
Kvetchers' cries
23D
Make _ ____ breakfast out of (really ruin)
24D
Peninsula shared by Italy, Slovenia and Croatia
25D
2017 American psychological horror film starring Jennifer Lawrence
29D
River found covering a large area around Switzerland [and literally within this clue]
32D
Loretta ____, American actress known for playing Major Margaret "Hot Lips" Houlihan on 'MAS*H'