I don't have strong opinions on this question, but here are some reasons you might think that "the", as it occurs in "the which", is semantically empty (that is, meaningless).
In prima facie support of this position, just consider that there are no plausible candidates for what 'the' could mean in these types of constructions (at least that I can think of).
Next, consider that the existence of semantically empty expressions is independently motivated. They are called syntactic expletives.
Some (for example, Haegeman) have argued that all syntactic expletives must occur in noun phrase positions (like the 'it' in 'it is raining'), thus ruling out that 'the' could be a syntactic expletive. But this is clearly not true given examples from Ancient Greek where the English equivalent of sentences like "The brown dog barks" would be "The brown the dog barks". In such examples, the second 'the' clearly serves no semantic purpose (it probably fulfills a syntactic role relating to case marking and/or signalling that 'brown' modifies 'dog', which would be important in sentences that contain more than one noun).
Further, some languages exhibit the phenomenon of preproprial definite articles (that is, in these languages definite articles necessarily or optionally precede names). Some linguists (Longobardi, for example) believe that such articles before names are semantically empty.
Further, there are even places in English where definite articles are, arguably, semantically empty. For example, some have argued that in expressions like 'The Nile' and 'The Atlantic', the definite article is semantically empty.
Given that 'the' appears semantically empty elsewhere, it certainly could appear empty in 'the which'.
Lastly, consider that as case marking disappears from a language, definite articles tend to appear (according to Hewson). If old English or its ancestor had case marking of relative pronouns like 'which', and these case markings were disappearing, 'the' might appear in a transitional phase. But that's probably a question for the linguistics SE.