Just to start a bit on the Jewish situation in general:

Why was Jewish settlement restricted to only a few large(r) cities?

Well, Sweden was an explicitly Lutheran country; there was not much pretense of religious freedom, and historically there'd been no Jewish minority; but the Enlightenment softened attitudes. The edict of 'general religious freedom' issued by Gustav III in 1779 meant that foreigners of other religions could freely immigrate and practice their religions, but Swedish subjects had to be baptized as Lutherans. The Judereglemente was the first thing to formally allow Jews a continued existence as Jews in Sweden. This was in part economically motivated; the idea was that competent Jews would immigrate and, thanks to their foreign contacts, engage in trade and specific professions that were in short supply such as polishing gemstones. And they were restricted to those professions. They were not allowed to practice agriculture, or any profession that was controlled by a guild.

It's worth pointing out here that not only was there little freedom of religion, but there was little freedom of trade at the time as well; a peasant doesn't get to work as a blacksmith just because he's good at it, if he's not a member of a guild and lives in a place where one exists. And just because you're a blacksmith and a member of a guild doesn't mean you're allowed to make a certain product if the king had granted a royal privilege of making that product to a certain town. And so on..

So in the POV of the time, there was no desire nor need for Jews in other towns, much less the countryside. As the Enlightenment won ground in the 19th century, the relaxing of regulations on what Jews could do and where they could live largely goes in tandem with the relaxing of economic regulations and the abolition of the guild system.

The year prior to Judereglementet, an Edict of Tolerance was proclaimed where foreign Christians were besides being allowed to practice their faith formally, were also permitted to raise their children in their own faith. However there was no edict covering other religions than Christianity and Judaism. Although Charles XII had permitted some Turkish Muslims to settle in Sweden and practice their faith there, that would not have applied to following generations, and so it was not until the 20th century any kind of persisting Muslim minority was established.

As for our sail-maker; I'm afraid Wikipedia has gotten basic facts quite wrong here; the town in question is Karlskrona (Carlscrona in contemporary spelling) on the southeast coast, not Landskrona in the southwest. The strategic importance of making sails there becomes apparent if you know Karlskrona was founded as - and still is - the main naval base and navy dockworks of Sweden.

The history is somewhat backwards too. the Jewish entrepreneur Fabian Philip, born in Mecklenburg, Germany in 1761 made his way to Sweden and ultimately Karlskrona in 1780, the year after the ban on Jewish immigration was lifted. There, he manged to establish himself as a cloth trader, over the protests over the local trading burghers. (complaints which seem to have been mainly motivated by hostility to competition, rather than outright antisemitism) He may have been benefited by the fact that, as a navy town, the burghers weren't the dominating social class.

In any case; Philip had not yet established a manufacture of sails when Judereglementet was passed, which would force him to move to Stockholm, Gothenburg or Norrköping. It was in reaction to this threat of being forced from his new home that he came up with a bargain, with the support of friends in the Admiralty: If he was granted an exception and allowed to stay in Karlskrona, he would stop trading and establish a factory for the manufacture of sails, woolen socks and other cloth items for the navy. The crown accepted this deal, although it took a few years before the capital was raised and the factory built, in Lyckeby just outside Karlskrona, where there was a river that could be dammed for power. But to the even-greater annoyance of his competitors, Fabian continued to trade in the meantime.

For most of Fabian's life, the factory was a success, employing about 600 people at its peak, including many recruited from the towns' poor. He was given a medal by the king for his work, bought a large town house. He became a member of a local literary society and seems to have integrated well into the town elite. To the extent that, in an era where Jews were (as said) prohibited from owning land in the countryside (until 1860) or living outside the cities, he was given dispensation by the Admiralty to buy a country estate - Afvelsgärde just outside Lyckeby. (recently declared a scheduled historic building, with specific reference to Philip's ownership)

However, by 1820 the fortunes of the factory waned; manufacturers in Gothenburg were producing better cloth cheaper, and Philip lost the contract. By this time they were established as landed gentry though.

The Jewish community in Karlskrona was never much larger than the Philip-Ruben family (through Philip's one child, Eleonore Ruben, who'd married a Jew from Hamburg). By 1860 it consisted only of 14 people, all members of the family except for the religion teacher (and acting Rabbi, it seems) Philip Lewin. The congregation would then grow a bit under immigration from Eastern Europe, and then decline again in the late 20th century, and declared itself defunct in 1994 citing aging membership and too few members to form a minyan.

Religiously it seems they were reform-oriented; the oldest book we still have that belonged to the congregation is psalm book from 1819 with commentary by Joel Brill (1762-1802), a Jewish Enlightenment figure. The later Jewish immigrants would be more Orthodox.

Harry R:son Svensson is the one who's mostly researched the situation for Jews in Karlskrona; see e.g.

The Case of Fabian Philip, Karlskrona’s First Jewish Entrepreneur: A Swedish Example of the Port Jews Phenomenon?, and

Den östjudiska invandringen till Karlskrona 1862–1920,

The naval city of Karlskrona and its Jewish entrepreneurs (paywall).

Really interesting account, thanks!!