The four groups resolve as follows:
Group 1: NYT 'Games'
Digits, Connections, Spelling Bee, The Mini.
Group 2: Prefixed by a compass direction
(Western) Union, (Northern) Exposure, (Southern) Cross, (Eastern) Standard Time.
Group 3: Involves 'diagonals'
tr(A) - the trace of a matrix, i.e. the sum of the elements along its main diagonal;
Diagon Alley - for the pun...
Bishop - the chess piece that only moves diagonally;
Hypotenuse - the diagonal of a right-angled triangle.
Group 4: Recurring memes/catchphrases from the Cracking the Cryptic YouTube channel
Three (in the corner, note) - "That's 3 in the corner... That's 3 in the spotlight - losing its religion";
Bobbins - Simon's go-to expression of annoyance when things don't go right;
The Secret - "45 is the secret" (the fact that the 9 digits of a sudoku total this number);
Maverick - the nickname given to a guy who seems to fly his plane nearby whenever Simon is trying to record.
(Big thanks to @Jafe for helping me understand this fourth category in chat, and to this fan-made reaction board, which also helped me understand!)
The connection between these four categories is not a single word. Instead it is the 'gimmick' of the puzzle itself, in that...
...each group of words appears in the initial grid in a way that is connected to their connections!
Group 1: The NYT Games words appear in the pattern displayed by its 'Connections' logo:
Group 2: The words prefixed by cardinal directions appear at the edges corresponding to the relevant points of the compass: 'Exposure' to the North, 'Standard Time' to the East, 'Cross' to the South, and 'Union' to the West.
Group 3: The words linked by 'diagonals' are on the main diagonal...
Group 4: And the remaining words relating to Cracking the Cryptic 'fill the cracks' left over (with 'Three' in the corner...).
The reason this would not be suitable for Only Connect itself is that...
...as soon as groups are correctly identified, their members are removed from the grid and the remaining options rearrange themselves into a rectangular grid once more - meaning that the words would no longer be arranged according to their innate patterns!