\section*{Supplementary Material}

The Supplementary Material comprises derivations of the equations given in the main text. Further, we provide additional data analysis on the statistics of the optical linewidths, as well as investigations in areas with different defect densities.
We present a proposal toward the generation of spin-cluster states. Finally, we outline the mathematics toward inferring the fidelity of generated the multi-spin states in the presence of photon loss. Moreover, we sketch a scheme for generation of spin-controlled multi-photon states.

$\,$\\
$\,$\\
R.N. acknowledges support by the Carl-Zeiss-Stiftung.
F.K. and J.W. acknowledge the EU-FET Flagship on Quantum Technologies through the projects ASTERIQS (grant agreement ID: 820394) and QIA (grant agreement ID: 820445), as well as the German Federal Ministry of Education and Research (BMBF) for the project Q.Link.X (grant agreement 16KIS0867).
J.W. acknowledges support by the European Research Council (ERC) grant SMel, the European Commission Marie Curie ETN ``QuSCo'' (grant agreement No 765267), the Max Planck Society, the Humboldt Foundation, and the German Research Foundation (SPP 1601).
T.O. acknowledges the JSPS KAKENHI (grant Nos. 18H03770 and 20H00355).
N.T.S. acknowledges the Swedish Research Council (grant No. VR 2016-04068). J.U.H. acknowledges the Swedish Energy Agency (grant No.  43611-1) and Swedish Research Council (grant No. 2020-05444). N.T.S. and J.U.H. thank the EU H2020 project QuanTELCO (Grant No. 862721) and the Knut and Alice Wallenberg Foundation (grant No. KAW 2018.0071).

\section*{Data availability}
The data that support the findings of this study are available from the corresponding author upon reasonable request.




