I would be surprised if Swedish law allowed for prosecuting a foreign company with not one bit of operations in the country.
You're joining two things here which I think are important to keep separate--the demand and the enforcement.
The Province of Bumbinga can absolutely claim worldwide jurisdiction and fine Apple $1T. And they can fine them a further $1T for every day they're not paid and their waterslide is not built.
Hell, _I_ could send Apple a letter claiming they owe me a trillion dollars so I can build a waterslide.
But when Apple doesn't pay a trillion dollars... then what? Send them angry letters? Still doesn't get the waterslide built.
A legal system's power isn't the orders it's the enforcement mechanism behind it. With a local presence they have the option to seize local assets and bank accounts, forcefully close operations, arrest employees, etc.
When the company has no local presence, your only enforcement mechanism is gaining the cooperation of a foreign country, in which case the country they're headquartered in is very relevant. And they're only going to cooperate if your request aligns with their ideals and generally benefits them.
Except in the most extreme cases, it's generally not worth it to try and impose your rule outside your borders because you have no mechanism to make anyone comply. It's an empty threat. Jurisdiction in the international sense is descriptive not prescriptive. It's recognition of the limits of your authority. The outcome is the same with or without it.
Signal may have users in Sweden which Sweden sees as giving it jurisdiction. Sweden may see it being accessible at all as giving them jurisdiction. Sweden may say "screw it, we have jurisdiction over the whole world!". But their ability to enforce that more or less ends at requiring ISPs to block their traffic or asking the US government to enforce their orders within US borders, so it's kind of a moot point.
Borrowing from how tax & law is usually applied for companies trading outside of their incorporated country, at least in many places including the EU: If you have users/customers in a certain country, even if your product is purely software, you can be considered to have operations in that country.
Couldn't users in pretty much every internet-connected country use VPNs and other methods of cross-borders indirection to access even those US services which explicitly block non-US IP ranges?
If this is the case, then is it not the case under the quoted reasoning above that any internet company should be expected to have operations in every other internet-connected country?
It's the same reason Australia and now South Africa demand payment from Meta and Google for revenues related to links going to local news sites and the like.
If no money is changing hands, good luck with that. (Or, rather, bad luck with that.)
(If money is changing hands, you might find your payments blocked by local payment providers, though even then that would take a while and might or might not happen.)
