I have some Catullus books that refer to 300 as "any formulaic large number" like how the Old Testament uses 40 days to signify a very long time, not literally 40 exact days.
-sources: The Poems of Catullus: a Teaching Text by Phyllis Forsyth
The Student's Catullus, Third Edition, by Daniel Garrison
If this statement about 300 being a stand-in for a large number, does this mean (could this mean) that there were not really exactly 300 Spartans defending Thermopylae, but just some great number?
It may be that 300 could be used as a formulaic large number in some contexts, but it seems unlikely in the case of Herodotus' or Diodorus Siculus' estimates of the Greek army at Thermopylae, since both use larger numbers for other groups - for example, Herodotus has the Tegeans and Mantineans both sending 500 soldiers and the Phocians 1000, while Diodorus has the Malians, Phocians, and Opuntian Locrians sending 1000 each. If they were using 300 as a formulaic number, it would be strange to see them use even larger numbers for the forces of other poleis.
EDIT: Also, please remember that, as my answer implies, there were far more soldiers on the Greek side of Thermopylae than just the famous Spartan 300.
Herodotus, Pausanias, and Diodorus Siculus all describe hundreds and thousands of other forces joining the 300 Spartans, for a total between 5,500 and 11,200, depending on the account. I don't think anyone suggests that 300 was the exact number of Spartans present, but it is likely representative of the actual number present.