You're right that this fascination with the Templars can seem a bit strange at first. They weren't the most successful military order (holy order is a misnomer, it doesn't actually describe a group like the Templars or Hospitallers, military order or military-religious order is the normal term). The Hospitallers and Teutonic Knights both established their own states. The Hospitallers only demilitarised in 1798. Up to 1918 the Teutonic Order fielded a regiment in the Austro-Hungarian army. Both orders are still around today. In contrast, the Templars existed for just under two centuries and never founded their own order-state.

The biggest factor that makes the Templars a greater presence in the popular imagination than these other orders is the Temple's suppression. They weren't "just another" order dissolved by the Papacy. The Templars were the first international military order to be suppressed and the only one to be dissolved on charges of heresy and after years of trials. Nothing like this had happened on such a scale before. The Order's end then allows for pseudohistory and conspiracy theories. What if some Templars got away? Was there a conspiracy against them? What if the Order still survives in secret? (it doesn't). Such stories are more difficult to create and spread when we know that an order survived, like the Hospitallers, or when few people know about another suppressed order. Who's heard of the Hospital of St Thomas of Acre? It's this dramatic end that is most important for the Templars' continued presence in the popular imagination, providing a memorable story and allowing for myriad myths and conspiracy theories to arise in the centuries after, further contributing to the popularity of the Templars.

In addition to this, the Templars were the first military order. The Hospitallers were founded earlier, but did not militarise until after the Temple was founded. They fought in every major engagement of the Holy Land crusades, which is the still the period of the crusades with the largest presence in pop history and pop culture. If someone reads a pop history on the crusades, it's going to have the Templars. The Hospitallers would probably also get a mention, but more minor orders like the Lazarites probably won't.

Also, the Templars were an important presence in medieval Britain and Ireland, owning many estates and acting as servants to the English and Scottish kings. The royal almoner in Scotland was traditionally a Templar. In England the brethren acted as royal financiers and diplomats. The English master of the Temple, Aimery of St Maur, was even a witness to the Magna Carta. They were fully part of the economic and political history of the medieval British Isles. For English-speakers, this increases awareness of the Templars and makes them more relevant to English-language pop history and pop culture than orders like the Teutonic Knights, Livonian Order, Knights of Santiago, Knights of Calatrava, and other orders that had no presence there. As pop culture is dominated by America, which largely draws upon English history when engaging with the medieval period, it's unsurprising that the Spanish or German orders are less prominent.

All of these factors have combined to create an order that had a dramatic and sudden end ripe for conspiracy theories, a prominent position in the best-known episodes of the crusades, and a greater relevance to English-speakers than more regional orders. Considering this, it isn't too surprising that the Templars are a much bigger presence in the popular imagination (in the Anglosphere, at least) than the other military orders.

The rise of far-right, Islamophobic hate groups and the recent obsession with the knights Templar is a more plausible idea than, "They did a bunch of cool stuff!"