Jerusalem always had more symbolic importance than strategic or commercial importance. There was some overland trade to and from Jerusalem, but it wasn’t very significant. For both Muslims and crusaders, the cities on the coast were much more important, since they led to European markets (and to Egypt since the sea route was faster and easier). For merchants in Europe, their ships would reach the cities on the coast first, so those cities were naturally much more important than Jerusalem, further inland.

This was true n the 12th century even when the crusaders still controlled Jerusalem. After the First Crusade they spent the next couple of decades trying to conquer the cities along the Mediterranean coast - Jaffa during the crusade, Caesarea in 1101, Acre in 1104, Tripoli in 1109, Sidon in 1110, Beirut in 1111, Tyre in 1124.

As you noted, after Jerusalem was captured in 1187, the government was re-established in Acre in 1191. Jerusalem was always a secondary target in future crusades. King Andrew II of Hungary tried to attack Jerusalem during the Fifth Crusade in 1217-18, but it wasn’t a very organized attempt and he just gave up eventually. In 1229, Holy Roman Emperor Frederick II did manage to take back Jerusalem - but he just asked the sultan of Egypt to give it back, there was no invasion. The sultans of Egypt and the sultans of Damascus were constantly fighting over it themselves, and it wasn’t really worth their time either.

This is a bit of a tangent, but it goes to show how unimportant Jerusalem was: no one was really happy with Frederick II. He was an enemy of the Pope and had been excommunicated before he left, so now the holiest city in Christianity had been regained by an excommunicated person. The church responded by putting Jerusalem under “interdict”, so masses and burials and other Christian services couldn’t happen there. They never moved the government (secular or religious) back there. Jerusalem was eventually pillaged and destroyed by some nomadic Turks from central Asia (the Khwarizmians) in 1244, and the crusaders never got it back afterwards. It had virtually no economic importance, it was all symbolic, for both sides.

It’s easy to see that Acre was the economic centre of the kingdom even before Jerusalem was lost the first time in 1187. In 1148, when the Second Crusade arrived, the leaders of the crusade and the leaders of Jerusalem met at Acre, not Jerusalem. The Moroccan traveller Ibn Jubayr noted all the merchant activity in Acre around 1184. The Italian maritime states also focused entirely on the coastal cities and never had any outposts in Jerusalem at all. The Venetians governed their own quarter of Acre, and in Tyre they controlled a third of the city. Genoa and Pisa also set up trade centres in the coastal cities. In the 1250s and 1260s, they even all fought an actual war over control of Acre (the “War of Saint Sabas”).

The Venetian governor of Acre in the 1240s was a guy named Marsilio Zorzi, who reported on the status of Venetian property there (and in Tyre), which helps us see how big and important it was. The crusaders also wrote some legal treatises, one of which was the “assizes of the burgess court” - the population of merchants in Acre was so big that they had their own court and their own laws, separate from the “high court” for nobles/aristocrats/knights. That book contains a list of all the products that could be bought and sold in Acre, and their prices - there are dates, onions, sugar, cinnamon, cardamom, nutmeg, linen, shoes…hundreds of other products, even marshmallows and licorice (they’re medicinal plants, but I always like to think they’re talking about the modern candy).

As a result there is a lot of work by modern historians about Acre and the economy of the crusader kingdom. The best place to start is probably the works of David Jacoby:

- "The trade of crusader Acre in the Levantine context: an overview" in Archivio Storico del Sannio 3 (1998)

- “The fonde of Crusader Acre and its tariff: some new considerations", in Dei gesta per Francos: Crusade Studies in Honour of Jean Richard, ed. M.Balard, B.Kedar, J.Riley-Smith (Ashgate, 2001)

- “Aspects of everyday life in Frankish Acre” in Crusades 4 (2005)

- “The economic functions of the crusader states of the Levant: a new approach”, in Europe’s Economic Relations with the Islamic World, 13th-18th Centuries (2007)

Some other books deal with the economy, although not exclusively…the two I am most familiar with (although they are getting rather old now) are:

- Jonathan Riley-Smith, The Feudal Nobility and the Kingdom of Jerusalem, 1174-1277 (Macmillan, 1973)

- Joshua Prawer, Crusader Institutions (Oxford University Press, 1980)

I hope that is helpful! Basically, the answer to your question is “no, Jerusalem was not very important”, but nothing really says so specifically - we can just see that it’s true circumstantially, because of how important Acre was and how they really only half-heartedly tried to get Jerusalem back (and then stopped trying entirely).