X will provide clues. [no to]
These cars belong to a category. [belong to a category]
X will provide clues to which category the cars belong.
One is hard pressed to concoct a mistake in The Economist's sentence:
Aston Martin’s IPO will provide further clues // to which category ultra-expensive carmakers really belong.
The parse is shown by the slash
belong to a category is a verb plus a prepositional phrase.
The sentence does not say:
Clues to a category. [clues to plus a noun]. That parse here would be wrong.
provide clues is a verb plus a direct object.
to which category ultra-expensive carmakers really belong=
a relative clause introduced by the preposition to followed by a relative clause introduced by which.
Typical of formal English.
placement of prepositions
Just one example from that link:
INFORMAL: Is that the man (who) she arrived with?
FORMAL: Is that the man with whom she arrived?