Determine the number of connected components of the odd-dimensional Ulrich-bundle moduli stack

Determine how many connected components the moduli stack of rank-[?] Ulrich bundles on a smooth intersection of two odd-dimensional quadrics has, beyond the explicitly constructed components.

Background

For a smooth intersection X of two odd-dimensional quadrics, the paper constructs multiple connected components of the moduli stack of Ulrich bundles by relating it to moduli spaces of parabolic bundles on the root stack P^1_{2g+1}. In rank two, at least $\binom{2g+1}{g+1}$ components are obtained. The construction does not exclude additional components, and the authors report numerical evidence suggesting that, up to degree-zero twists, the explicitly constructed components may be all the components in rank two. The general number of connected components remains unresolved.