How can I improve at seeing mating patterns with seconds on the clock?

Writing this at 2:00 AM after a late-night bullet spree gone wrong. I view this disappointing loss as a turning point from my steady upward climb to the subsequent descent out of the 2200s. In the final seconds, my opponent moved his king out of pawn cover to avoid the perpetual check I was trying to perform and suddenly I had an opportunity to do more than just get a draw. I could sense that checkmate was near but I just could not see the pattern quickly enough and I lost control of the position:

The winning sequence is a fairly easy mate in two—37. Qg4+ Kh6 38. Qh4#—but I simply could not see it in the time pressure rush. At the initial Kg6?? advance, I had 7.5 seconds remaining, and the first move I played was good (f5+!) but it fell apart after that.

So in general, how can I improve in these types of situations where I am actually trying to make something work in the final seconds and am not just mindlessly bleeding the clock?

"7.5 seconds" is going to definitely affect your psychological thoughts. If the checkmate didn't actually exist, you would probably lose on time. In time trouble, these things do happen. What appears obvious to us may not be the case in time trouble.

Most exam candidates would panick upon realising they have minutes left. If you manage to see a candidate with only half of a two-hour paper completed and still write slowly and calmly with two minutes left, that would be awkward.

True, but to a degree only, in part due to the fact that we know that there is a winning line involved in a specific puzzle, whereas there may not be such "winning paths" in an actual game.

Performance also varies from players to players, with some players being able to handle pressure even with only two seconds left on the clock and some others panicking with ten seconds left.

I'm far below your level but I think it comes down to focus on mating nets. There's a book called "The art of attack in chess" by Vladimir Vukovic which can help you with nets and focal points.

I believe the OP is familiar with the mating nets, but is more concerned about the psychology of the handling of time trouble.

The only way to perform better under stress is to excercise to the point it becomes second nature. I have the same issue. I panic when I'm getting low on time and i completely lose track of where my pieces are, especially when I'm winning against a higher rated player. I think it's hard to improve on that aspect other than keep doing speed puzzles over and over.  Some parts of your personality will always stick with you. Good luck.

A classic.  Get it.  Study it.  You will not regret it...

The Art of Checkmate by Georges Renaud & Victor Kahn

https://www.amazon.com/Art-Checkmate-21st-Century/dp/1936490846/ref=sr_1_1?crid=BDVGY8R5ZS74&keywords=art+of+checkmate&qid=1673593400&s=books&sprefix=art+of+check%2Cstripbooks%2C168&sr=1-1

from the internet (Scribd.com).....an accurate review of the book...

The Art of the Checkmate By Georges Renaud and Victor Kahn...
"The art of the checkmate has at last been provided with a scientific foundation." — Chicago Sunday Tribune
One of the most difficult situations in chess is seeing potential mates in the near future. All players, even grandmasters and champions, have missed such mates in actual play, to their chagrin and the bystanders' delight, for all too often it is easier to play for momentary advantage than to force a mate.
This book by two former national chess champions of France provides a rational classification of mating situations, and shows how each possible type of mate has emerged with its variants in actual play. In an examination of 127 games, the authors identify 23 kinds of mate and show you the rationale for each. These include among others Legal's pseudo sacrifice, the double check, the smothered mate, Greco's mate, the Corridor mate, Anderssen's mate, Morphy's mate, mates with heavy and minor pieces, the mate of two bishops, of two knights, and many more. Review quizzes with answers are included, so that you can gauge your progress.
Since this book analyzes ideas rather than setting memorization tasks, it will enable you to see basic patterns, give direction to your game from the earliest moves, help you to foresee forced mates and counter effectively, and most important, improve your style of play so that you can force mate.
"The Art of the Checkmate will surely be a valuable addition to the library of any chess fan."— Springfield Republican

Also excellent are  "1000 Checkmate Combinations" by Viktor Henkin and "Fundamental Checkmates" by Antonio Gude.

7.5 seconds is enough for 7.5 moves at bullet speed, not even counting pre-moves.

Being familiar with some mating pattern will help you spot such patterns in a game even with little time on the clock.

@AgentGPx34, in this position it was mate in 2 which you missed and lost a pawn, then your queen and eventually the game. 

Instead, you played this.

But it's ok, bullet can be very panicking especially when you're winning and your time is low so never mind, winning and losing goes on.

And in such situations I advise you to premove safely, meaning which would not effect your position and then wait for the opponent to timeout because you have to be faster, it has happened to me when I was up a queen vs a lonely king but with 5 secs I can't mate him so I become Usain bolt and started making safe premove to save timeout, stalemate and capturing the queen by his king etc. I was faster so he time outed and I won.

get better at tactics lol?

- How can I improve at seeing mating patterns with seconds on the clock?

Here's how I would do it:

First get better at spotting mating patterns in puzzles and slow games, and then transfer those skills to Blitz and Bullet.