The situation is more complicated than the other answers suggest. You are dealing with a "complex sentence" that contains two distinct clauses, one embedded in the other. The "matrix clause" has the subject "Technical analysis and debate" and the predicate "are what matter(s)". The embedded clause has the subject "what" and the predicate "matter(s)".
So the subject of the verb "matter(s)" in this sentence is not the plural noun phrase "Technical analysis and debate", but the pronoun what. The word what does not inflect for plurality. In a clause that has what as the subject, the verb usually takes singular inflection, even if what is meant to refer to multiple objects: we can say things like "They don't know what is in the bags", but we can't say things like "*They don't know what are in the bags". But in some cases, what can take plural agreement.
The following "Grammarphobia" blog post provides a summary of what some resources say about how to inflect verbs for grammatical number when what is the subject: When the complement was roses. Unfortunately, none of the examples discussed there seems exactly parallel to the sentence that you mention. They say that "what" can take plural agreement when it has a plural predicative complement in the embedded clause or in the matrix clause, but in your sentence, "what has no predicative complement—rather, "what matter(s)" is being used as a predicative complement of the subject of the matrix clause "Technical analysis and debate".
But some of the sources do bring up notional agreement. As Sahil Agarwal's answer and Charl E's comment suggest, if you choose to follow notional agreement here, the use of plural are in (your version of) the matrix clause seems to point towards using a plural verb in the embedded clause as well. If you use is in the matrix clause, as Jared Hooper suggests, it seems clear that you should use singular matters in the embedded clause.
I would recommend using whichever form sounds most natural to you.