its never mentioned again... but any idea how the message at the end of the episode affects the academic and scientific community in the federation and elsewhere?
The only sequel I know of to this directly was in a video game.
I wrote a synopsis for a sequel which is my only fanfic type story ever. I'm not really a big fanfic reader so I don't expect people to want to read mine. Though I think it would have made the best ST movie ever.
Obviously The Chase is important on many levels. In-universe it explains the human centrism we see on screen. In reality it gives us a conceit for the limited makeup budget. In-universe it gives us an underlying epic scale, touches upon a race like the Preservers from TOS, and expands ST into a timeline much like any good world building universe like Larry Niven's Known Space, Brin's Uplift, Iain M. Banks Culture, etc.
Like another long-time scifi example in season 5, the Dyson Sphere, the discovery in biology would probably have a huge amount of resources thrown at it, and would probably pick up the threads more quickly than just one man could have done.
Culturally, there may be some in the "enlightened" 24th century, even allies that would not like the implications. Eventually I think finding out we are all more related than we thought would bring a certain sense of appreciation to all the affected races.
We already saw that the Yridians and several enemies of the UFP were ready to fight over the information, it might be possible that any other "secrets" discovered would also.
For Star Trek as a TV show, The Chase is clearly the signature piece of the franchise as a whole, it brings almost all the major players of the time and ties them together with a brisk "chase" plot (combining the Sagan "Contact" element of finding universal clues in a long calculation for Pi and a Mad, Mad..World)...so it has good character moments for Picard, action, philosophy, a healthy dose of humor, and a perfect Trek ending..the Romulan captain calling Picard which suggests a light at the end of the tunnel of conflict with each other.