  A majority of massive stars are part of binary systems, a large fraction of
which will inevitably interact during their lives. Binary-interaction products
(BiPs), i.e. stars affected by such interaction, are expected to be commonly
present in stellar populations. BiPs are thus a crucial ingredient in the
understanding of stellar evolution. We aim to identify and characterize a
statistically significant sample of BiPs by studying clusters of 10-40 Myr, an
age at which binary population models predict the abundance of BiPs to be
highest. One example of such a cluster is NGC 330 in the Small Magellanic
Cloud. Using MUSE WFM-AO observations of NGC 330, we resolve the dense cluster
core for the first time and are able to extract spectra of its entire massive
star population. We develop an automated spectral classification scheme based
on the equivalent widths of spectral lines in the red part of the spectrum. We
characterize the massive star content of the core of NGC 330 which contains
more than 200 B stars, 2 O stars, 6 A-type supergiants and 11 red supergiants.
We find a lower limit on the Be star fraction of $32 \pm 3\%$ in the whole
sample. It increases to at least $46 \pm 10\%$ when only considering stars
brighter than V=17 mag. We estimate an age of the cluster core between 35 and
40 Myr and a total cluster mass of $88^{+17}_{-18} \times 10^3 M_{\odot}$. We
find that the population in the cluster core is different than the population
in the outskirts: while the stellar content in the core appears to be older
than the stars in the outskirts, the Be star fraction and the observed binary
fraction are significantly higher. Furthermore, we detect several BiP
candidates that will be subject of future studies.
