I think in response to OP, any female in a High School setting with significantly higher testosterone levels than an average healthy teenage cis female, is likely to have an advantage in most athletic competitions, which could be a significant advantage.
We know from sports like powerlifting where testosterone supplementation, anabolic steroid use and etc is widespread, that in men, the higher you shift your testosterone the stronger you get, the better you recover etc. A famous lifting coach once was asked why people use steroids and his answer was “because they work.” They aren’t woo. Anabolic steroids drive hormonal changes that make you stronger and better at most sports.
A High School cis female who has significantly higher testosterone levels, knowing little more about the specifics, almost certainly has a significant physiological advantage over biologically average cis females. In fact this biological reality is why we have gender segregated sports, if by some quirk in human biology women had more manlike testosterone levels (but somehow maintained their ability to reproduce, i.e. assuming a generally different human biology than exists in our world), the performance difference between women and men would almost certainly be much, much narrower (there may still be some advantage to biological males due to other factors.)
As an illustrative point I reference Mark Henry, recently retired WWE wrestler who got his start as a powerlifter in the 1990s and was on the U.S. Olympic weightlifting team. He is among the most, if not the most, genetically gifted strong person in measured human history. He is also one of the few people in the strength sports who is widely believed to have never used PEDs of any kind.
As a High School senior in Texas in 1990 (and no lifter hits their genetic potential in HS, most don’t until their late 20s/early 30s)–raw / without using straps or equipment, Mark performed a competition squat of 832 lb, bench press of 525 lb, and a deadlift of 815 lb for a combined powerlifting total of 2033 lb. These numbers would remain world records if he were a woman, at any age, by over 200 lb in the squat and deadlift and by around 75 pounds in the bench press.
Women’s powerlifting is a much smaller sport than men’s powerlifting for a number of reasons, as a frame of reference many women’s records are held by a 30 something woman named April Marsh, who was born biologically female, but is widely known to be taking massive amounts of testosterone supplementation, anabolic steroids, HGH etc (she has developed severe male pattern baldness and other signs of serious abuse of performance enhancing drugs.) She’s the one who is still over 200lb behind Mark’s records in two of the lifts, and the next woman below her is quite a bit further behind Mark.
TLDR high test = advantage in sports, and any serious person will acknowledge this.
So what does that mean for High School athletics? Transmen, who likely want to compete in boys sports, would pose little competitive issue doing so, and would likely pose serious competitive issues if forced to compete in girls sports, as assigned females at birth who are taking hormone treatment that raises their testosterone level, they would almost certainly have an unfair advantage against cis females. Additionally, they almost certainly want to compete in the boys sports as they identify as male. Additionally, they are likely to still have disadvantages versus cis males, so they are not going to have any kind of advantage in the boys sports from their hormone treatment, if anything being born with female sexual anatomy they almost certainly will still have a disadvantage in boys sports.
Note that many schools attempting to regulate this are forcing transmen to still compete in women’s sports, which actually is likely one of the more “unfair” things to the non-trans athletes that is out there, and it is being caused by misguided conservative moral panic.
Transwomen are the more complicated matter, since we do know that if they are under hormone treatment, they will be at a serious disadvantage against cis boys, but they likely will retain some advantage over cis girls, specifically because at the ages involved in High School it is not likely they have been undergoing hormone treatment long enough to hit the IOC Olympic guidelines that allow for transwomen to compete in the Olympics. Is this a serious issue? To me it frankly isn’t. Transwomen who want to compete in girls sports are only a % of all trans people who are a very small % of people in general. I think someone going through rough personal times with their sexuality being allowed to compete in a sport isn’t the end of the world even if they do have some advantages.
I do think it’s a rougher situation though, while High School sports are small beer to many, for the families and kids involved in them they are a big deal. I actually think in some of the documented cases, transwomen have actually been willing to play on the boys team (especially because in many places, boys teams are somewhat of an “open” team, for example where I grew up there was no girl’s wrestling team, there was only a boy’s, and a couple girls actually did get on the team, I think this is still common in areas without big wrestling teams, in most places girls can try out for the boy’s basketball and football teams, although they will almost never make those teams), laws to prevent this for transwomen are ill considered. But the transwomen who are receiving hormone treatment and want to compete in girls sports? From a utilitarian standpoint I think the moderate advantage that person might have is outweighed by the serious emotional and social harm in being excluded from sport in the gender of their choice. The weighting of that would change past the High School level (i.e. college / olympic sport, where the competition is frankly much more important.)