It is around time of ST:ENT S4 where one of its plotlines suggests an explanation for that era:
The rather militaristic Vulcan Navy was being manipulated by Romulan agents. After our heroes recover the teachings of Surak, and uncover some of the corruption (but not the Romulan connection), the Vulcans have a radical change of heart and move toward their TOS attitudes.
However, Vulcans retain their own intelligence service at least through TNG era.
Vulcans have starships. It’s just since the founding of the Federation that they rely on Federation ships for “military purposes” to extent that post ST:ENT Vulcans have military purposes. Vulcan ships appear in the films: in ST:The Motion Picture, the Enterprise rendezvous with a Vulcan shuttle to collect Spock. Vulcan ships are also seen through TNG series.
But while they have starships, they have not generally maintained an armed navy.
TOS: “The Immunity Syndrome” starts with Spock "Feeling" the all Vulcan crew of the Federation Starship Intrepid die. Vulcans are both assigned to Federation crews, and in some cases, the entire crew of Federation ship is Vulcan. In any case, these are plumb resources for the Vulcans, as it was mentioned that the Intrepid was the only Federation Starship manned by Vulcans; also Kirk has suggested there are only 12 of the class in the fleet.
There were also indications that the status of a “military fleet” may have been changing by end of TNG era as seen in “Unification, Pt. 2.”
In this episode, the Romulans stole Vulcan ships to confront Romulan ships and were full of Romulan shock troops ready to sneak attack in a surprise attack under a false gesture of peace. Why it was not a surprise that Vulcans would send a flotilla of their own ships and not a Federation ship is not explained, nor confirmation of a move by Vulcan further towards or away from maintaining their own “military” fleet.