There is absolutely a sustained advantage to trans women long term. Anyone saying otherwise has their head in the sand.
It's obvious this is unfair for cis-gender women. Even a tiny minority of trans women can make traditional women's sports irrelevant. And this is just on the college/pro level.
On the HS level there is no ability for high school athletic associations to monitor hormone treatment or verify transition. You are going to see exactly what happened at the Connecticut state championships in the 100 in 2019 over and over again. High school girls will repeatedly be dominated by transgender athletes.
This highlights the problem: It only takes a tiny number of very average transgender athletes to break the HS system. A transgender girl who as a boy ran a 4:40 1600 would dominate any state championship not only in the 1600, but also in the 3200 and 800.