From a comparable project, Georgia State University's Center for High Angular Resolution Astronomy ([CHARA](https://en.wikipedia.org/wiki/CHARA_array)) interferometric array was constructed for about $15m in 1985. That facility has six one-meter telescopes. That would be about $45M in 2024 dollars.
While I cannot attest for the accuracy of the cost estimate, I can note that the BFT takes several approaches which I think will help control costs. In particular, they are leveraging a multitude of proven technologies, COTS components, and smaller telescopes.
In case anyone is interested in learning more about this star, Dr. Brad Schaefer wrote a nice article about it in the March 2024 issue of Sky and Telescope (subscription required):
My organization, the AAVSO, has material that can help you learn how to observe variable stars and make scientifically useful measurements. You can do this by eye, with binoculars, with a telescope, or with various digital sensors. In the case of T CrB, visual observations will yield very useful information. Please see https://www.aavso.org/tutorials and https://www.aavso.org/observing-manuals for more information.
Suburbs aren't as bad as you might imagine. I observe from my patio under Bortle 6 skies (you can looks yours up at https://flexspec1.readthedocs.io/en/latest/) with a 5" telescope. We use to have a robotic telescope located in Cambridge, MA and it produced useful science.
As you mentioned, astronomy is a field where contributions by amateurs / citizen scientists are extremely valuable. A few organizations that exemplify this are: (1) the American Association of Variable Star Astronomers (disclaimer, I'm their Executive Director) which collects photometric (brightness) data as well as spectroscopic data on variable stars and kindred objects including exoplanets (2) the Society for Astronomical Sciences which is more broad than AAVSO, but with a moderate focus on instrumentation (3) the Center for Backyard Astrophsyics (hyper specialized on one type of variable star, a good collaborator of the AAVSO) (4) the International Occultation and Timing Association that observe asteroids occulting (blocking) stars to infer their shapes
Most countries have organizations similar to these too.
Edit: There is a group within the SAS working on an automated optical spectrograph for astronomy called the FlexSpec 1 (https://flexspec1.readthedocs.io/en/latest/). It is about $500 in parts. Similar devices sell for about $3,000.
While I cannot attest for the accuracy of the cost estimate, I can note that the BFT takes several approaches which I think will help control costs. In particular, they are leveraging a multitude of proven technologies, COTS components, and smaller telescopes.