First see footnote 1 of the first page of the preprint linked at the top. The authors are jumping the gun. That's fine for theorists, but bear in mind that they are literally in the dark on a number of telescopic observables, any of which would shoot down the idea in the preprint. Some of these are achievable by EHT. See e.g. Olivares et al. "How to tell an accreting boson star from a black hole" (2020) <
https://discovery.ucl.ac.uk/id/eprint/10112389/1/staa1878.pd...> [pdf].
The exotic bosons available in a 3+1 spacetime have never been detected at energy levels low enough that one might expect them to be reasonably bound by the weak (yes, weak) gravitation required by the boson star's internal repulsive forces. If the internal repulsive forces are too weak (or their self-gravitation isn't weak enough), the bosons cannot support the star against ultimate gravitational collapse (into a black hole). If the internal repulsive forces are too strong, the bosons all escape rather than stick around in the neighbourhood of the star. The latter is especially acute since the boson masses considered by the paper may be smaller than that of neutrinos.
Until a suitable slightly self-repelling exotic boson is discovered, achieving and maintaining equilibrium between it and gravitation is pretty fatal to the boson star idea.
Cold massive bosons are an idea for particle dark matter, incidentally. An example dark matter candidate is the axion. Axions have not been convincingly observed, and might not exist. A compact object made of essentially only axions could plausibly meet the criteria in the preprint linked at the top (cf their axion-motivated scalar field equation at eqn (9)), depending on details of heating during gravitational compaction. Also see e.g. Mohapatra et al., "Dense Axion Stars" (2016) <https://arxiv.org/abs/1512.00108> which is the preprint version of the PRL letter <https://doi.org/10.1103/PhysRevLett.117.121801>. There is as far as I know no clear mechanism to have anything like the axion density required for self-gravitation except in the very early universe, a long time before the first galaxies. So then why would small primordial axion stars be in galaxies, as the binary in the article at the top appears to be? How do you keep them small, rather than coalescing into supermassive compact objects?
The preprint at the top discusses other Beyond The Standard Model (of particle physics; BTSM) possibilities, but they are less convincing than the axion (for starters, such BTSM extensions need to have some non-physical degrees of freedom strongly suppressed, since such BTSM theories are almost always "haunted" by <https://en.wikipedia.org/wiki/Ghost_(physics)>s.). Additionally, the axion is motivated by the strong CP problem in the Standard Model, and if there is a lot of them they become gravitationally relevant. The non-axion options in the preprint at the top are afaik only motivated by a lack of knowledge about the microscopic details of gravitational physics. (See Koberlein's 2021 blog entry on Proca Stars <https://briankoberlein.com/blog/proca-stars/> for a brief intro to (light) massive vector boson stars).