Biological differences are not a mere social construct, because plenty of evidence can be used to tie the perception of these differences not to "opinions", but rather the way our senses work. E.g. toddlers already recognize beautiful faces from less attractive ones.
OTOH it's possible to generate social beliefs around biological differences, which are opinions, but not necessarily true deciptions. An example would be to claim that members of group A always have [a negative characteristic]. This is stereotyping and a central cornerstone in practical racism. Because it causes people to be prejudiced against based on group characteristics.
It's about a bit both. Social constructions in the sense of biases that follow from quick stereotyping (all fat people are lazy). Something else based on psychobiological evidence on how our senses and brains discriminate things.
One should perhaps also question the concept of race, since it may allow multiple definitions. Then the question is too broad, since some definitions might be more social and some definitions might be more biological. Based on e.g. Merriam-Webster definition:
any one of the groups that humans are often divided into based on
physical traits regarded as common among people of shared ancestry
For there to exist races would require that not all are inherited from the same ancestry. OTOH one would argue that this definition is too broad, if it assumes that racial differences must be determined from some (possibly hypothetical and not truly determinable) original ancestor.
One could also point out that "anti-racism" is also at least partly fueled by "designated" propaganda, which may be aimed to discredit racist beliefs, but which may not as such be "science-capable definitions". Such as lifting/modifying the argument that racial differences do not exist, because there's not enough variation:
https://www.psychologytoday.com/us/blog/looking-in-the-cultural-mirror/201109/the-main-reason-races-don-t-exist (now this may be valid science as such, but it may be applied in biased ways)
But I find that it's fundamentally still a matter of definition.
It's also important to note that:
social races exist--though racial systems of classification differ from one culture to another--and form the basis for unequal treatment of differently categorized groups
I.e. the idea of social hierarchy changes.