Best DAC for around $2,500 or less

This should be easy, go over to ASR and filter the database by SINAD for the money, done.

I wish I could say that it was that easy for me.  If that were the case, I'd have the Benchmark hooked up and sold the BorderPatrol.  Turns out, my preferences don't align to perfect measurement... but when you really think about it, I think most people don't.  Not a perfect analogy, but I bet everyone here also knows someone who (some what annoyingly) way overuses Instagram filters in their photography.  Is that a more accurate representation of the picture?  Definitely not.  Does it give them some joy / describe a mood / something else emotional the original did not?  Likely.

There is no ’Best’, and really no way around trying to figure out what your own preferences are based on listening.  Someone's "this DAC is overperforming over that DAC" comment need to be taken in context that their definition of overperforming may not be yours.

I currently own all three of below, and appreciate them all in their own way:

Chord 2Qute (predecessor to the Qutest, which likely is another level of improvement) - may daily driver in my ’main’ system of Naim 282/250/ATC19s because I love the balance between great insight while still feeling a certain drive and ’verve’ (sorry, terrible word) to the music that keeps my attention

Benchmark 2 (currently used as headphone amp, not in a system otherwise) - wow, the most insight/clarity/detail out of any of the DACs. it’s remarkable what details it can pull out of tracks you thought you knew. But for day-to-day listening, it is *not* my preference, so important to understand what may sound most technically accomplished may not be what you prefer day in and day out

BorderPatrol SEi (currently in my office w/ a Supernait 2 and ProAc Tablette 10s) - probably listen to as much if not more than my main system during this WFH era, and I absolutely love this DAC, especially with the tube engaged in the rectifier. Yes, it doesn’t do high rez, and yes I know it has crap measurements in Stereophile... but I can listen and love Roon streaming in background for hours a day and every once in a while between meetings really crank it up and I am in heaven.

All of which is a long way of saying, absolute $s and tech specs can’t tell you what you’ll end up liking. Consider buying used (or something new with a healthy secondary market), because odds are you will learn more about what you love over time, and experimenting is part of the joy. 3 years ago even, I wouldn’t have known all of above when I first bought the 2Qute, but I dipped my feet in with the Mojo, loved that, and my appreciation for Chord has remained. ¯_(ツ)_/¯

DAC's aren't at all like Speakers, or even Power Amps when it comes to adding flavor to sound systems. 20 years ago, when I was young and impressionable I might have agreed with you, but when the goal is converting 0's and 1's to an analog waveform, measured performance really should be king, imo. If you want to add a sonic signature that you find pleasing to your system I feel like the equipment to do that with are primarily speakers, followed by amps.

Does that thinking translate to cartridges?  After all, they are a source too. It's an analog-to-analog conversion, but to stay logically consistent, why should deviation from accuracy have any place there either?

This is a hobby entirely of personal preferences -- and I assume most people put their enjoyment of music over the accuracy of a given piece of equipment's measurement.  I would never claim the Border Patrol is the most accurate DAC – I 100% trust the measurements that say it is not.  But given I have a Benchmark DAC sitting inches from it, and have put 100s (maybe 1000s?) of hours into listening to both, in same system, I feel pretty confident knowing which one I enjoy more.  For arguments sake, I could even buy someone saying "there's a mental trick/placebo thing going on and you are fooling yourself" and my response would be "OK, maybe you are right... but I'm not looking to cure cancer with this DAC, and if I'm fooling myself into this much pleasure, please don't give me the real medicine if it lowers my enjoyment"

And isn't maximizing enjoyment ultimately the dimension that the OP is most likely aiming for within the $2,500 budget?  

Of course, if the question was "which is the best measuring DAC where I can be happy with the graphs it produces?" then we are having a totally different discussion and I'd only point to the BP as what *not* to do.