In general, the less people know about your world, the better. The fact that your universe has wormholes, is completely irrelevant. All we need to know is that 'travel between upper (space station) and lower (airports) atmosphere has become so commonplace as to be its own transport industry (like boats or airplanes).
You're question includes snippets that people can latch onto that aren't relevant like
"it is economically favorable"
For who? Just like with cars, you can make a cheap piece of *@# that requires constant part replacements, or an expensive bulwark that won't need a dime for centuries (aside from gas) and is cheaper long term (gas vs solar energy for example).
"assume for simplicity that the atmospheric conditions around each wormhole are Earthlike (sic) at sea level"
Why do we need to enter orbit then?
Invites alien tech even though you want a modern tech solution.
"While one side of a wormhole may be in the upper atmosphere, the other may be hundreds of kilometers deep in a jovian counterpart, unfit for entry or exit.)"
I'm sure Physics.SE would just have a field day with this.
So this is why generally "less is more". The less information to shift through, the clearer the question being asked is, and the less side details to be distracted by. The extra world details also invite Frame Challenges (alternate solutions/set-ups to the presented problem). If you wanted a solution, this would be a good thing; but you aren't looking for a solution, but a cost effective design.
Sometimes the world fluff can be good to include. It can be a fun way of explaining things like the tech level, magic level, general world attitudes, and the like without just listing a boring bullet point list. But you need to review that fluff carefully and make sure it also ties directly back to the main question so the reader doesn't get lost on what the point is.
I recommend after writing a question you play your own devils advocate, and read it again finding every question a new reader may want to ask, even if it's not directly related to your main question. Every question you think of, some else will want to bring up. Either address it, or remove that detail from your question.
The other half is it's not just your question, but how you ask it. "what re-entry technologies would likely be employed by ..." the words "would likely" imply that you want speculations on driving market factors like, availability of materials from other worlds, environmental concerns (or lack thereof), ect. Avoid wishy-washy words in your questions like "likely" or "would" or "could". Your questions should come off as asserting the base facts are indisputable. So for example, "What is the least maintenance design for rapid re-entry vehicles?" or "What is the cheapest modern design for rapid re-entry vehicles?" (long vs short term is still debatable, but the question is at least worded in a way that an answer has to challenge you on that if they want to bring it up)