The term minimum fuel to me means that I’m advising ATC that I’m now going below my minimum diversion fuel, ie. I’m now COMMITTING to my choice of airfield. Any delay or indeed closure above that alread advised when I make that advisory will require a Mayday call (not a Pan) as ANY diversion will require landing below minimum final fuel on aircraft (30 mins).
In making that decision I should consider delay to approach advised, weather, expectancy to land at my now committed airfield.
Yes it’s an advisory message, but I expect ATC to appreciate and bear in mind the consequences of any further delay to that already advised or airfield/runway closure.