The Ohr Hachayim Hakadosh writes that the Halachos were a Mesora and Chazal were doing backwards engineering to find where it is Merumaz. This approach is Mefurashh in the first Amud of Megilla, when we are dealing with a Derabanan and we even knew the reason yet the Gemara says there must be a Remez in the Megilla, and the Sugya goes hunting that Remez.
This is pretty much the normative approach in the Drashos Chazal. There are times when Tana’im argue and bring proof from Pesukim, but that might just be as proofs and not their source.
However, the Gemara says that when two Dayanim agree to a Din, yet they learn that Din from a Different Pasuk, they don’t get added together for the majority counting. This shows that the Pasuk is actually the Mekor of the Din. The Maharal also is adamant that the Drashos actually show us the Halacha and that even Asmachta Be’alma is an actual reason for the Derabanan.
Therefore, it is reasonable to say that it is both. The Halacha was a tradition and the Drashos weren’t always passed down together with the Halacha, but they are the actual source, no doubt. Each one helps the other one where the tradition got flaky.