Engine is still need development its not perfect as you say.
Brilliant Moves in New Game Analysis Report

Gentlemen,
You keep trying to define what a brilliant move is. Here is the definition:
"A brilliant move is a move that was not foreseen by the engine and brought better results than those foreseen by the engine."
Q: How did the engine identify it as brilliant?
A: After you actually made the move, the engine compared it with its analysis of best moves (prior to your move). The engine evaluated it as better. Voila! it is Brilliant.
Q: How come the engine did not foresee it?
A: You all know that the next move analysis requires navigating into a tree of moves. The brute force tree is so vast with perhaps millions of moves. Hence the engine does some optimization and goes into a limited set of moves (a smaller tree) based on some "value-based" search algorithm. The brilliant move would have been found by the engine (hence would have never been identified later as brilliant) if the algorithm was optimal; i.e., perfect. The algorithm is suboptimal; i.e., a little less than perfect.
Q: How can you learn that my definition makes sense?
A: A course in AI (with some focus on search algorithms, with some focus on value-based search algorithms in particular, with some focus on 2-players games value-based search in particular) would lead you to the same definition. Hint: search for Alpha-Beta search algorithm.
Cheers
I don't have a definition for brilliant move BUT I want to help you define it by telling I got a brilliant move at just move No.7.So I think it's not about the depth!

This game is old but I still don't know how that is brillant.
Game: https://www.chess.com/analysis/game/live/37727359771?tab=review
my game at 1200 having a brilliant move !!!
https://www.chess.com/analysis/game/live/40909788601?tab=review

Brilliant moves outranks best moves.
Best moves are the moves found and assessed as best by the engine (whether you played it or not)
Hence brilliant moves are only made by the human player.
The engine assesses a move to be brilliant only after it is played (can never be proposed as mentioned above).
The engine was capable to assess a move to be brilliant in comparison to its best move when it is played by finding the outcome to be better than the engine proposed (its best move).
Hence a brilliant move is one that is proven to be best only if the engine had gone into a depth that is further than the depth it traverses, but it does not. This is why it can only figure it out after it is played by the human player.
¨Hence brilliant moves are only made by the human player.¨
Sometimes I watch some engine chess video where stockfish plays vs Alphazero and then they both make brilliant moves (seing in the analyses)
So I still don't really understand the definition of "brilliant¨......

Two Different Games!! Back to Back! 2 In a row(each game)!! Games were weeks apart
Different Setup! SAME EXACT SQUARES AND PIECE!! WHAT ARE THE ODDS!! ASTRONOMICAL!
https://www.chess.com/live/game/40762198753
https://www.chess.com/live/game/31143590851
A brilliant move is a move when the engine is oblivious to the move's potential in the future but after the player plays it, then it realises the potential that the move carries. As a result, it marks it as a brilliant move as the engine was unable to analyse it correctly.