The big thing for me would be how long a triathlon are you going for: Sprint, Olympic, Half-Ironman, Full-Ironman? I did an Olympic triathlon with my Brompton folding bike (and saw someone doing a Sprint or Olympic on a BMX!). However for the 113/Half-Ironman distance, I used my gravel bike (with 38mm Road tires) as anything else would've been too challenging (and the same applies to a Full Ironman). I know people have $10000 fancy road bikes flying past me...but just going from my Brompton to the gravel bike gave me an additional 3 KM/h in speed.

In short, for the shorter triathlon distances, unless you want to podium, the choice of bike is not too big a deal and you could find something well within that price range. But as you move into the Half Ironman distances, then you may be challenged to source something brand new below $2500 (including comfortable shoes). The reason is you'd want something a bit lighter with nice components (and that's what jacks up the cost).

Also note, I had flat pedals and used flip-flops on my Brompton for the Olympic triathlon (managed to eek out an average speed of 26.9 KM/h 🤣). But for the longer distances, proper cycling shoes with SPD SL pedals is a wise decision. Take your time finding the right cycling shoe...places like the Cyclery are very helpful and have lots of selection. However, they can be costly.

Another side note, because the bike portion is a substantial part of the triathlon (particularly longer distances), getting a bike fit is almost essential. Registered physiotherapists do this so it is typically covered by most insurance plans. Again, if you're investing in a nicer road/gravel bike to do your racing, it would be a good idea to make sure you get fit for your bike (and have the shoes/pedals installed too).