Tesla punk also including technologies from the late 1800s will allow for technologies such as basic radio communication, also radio altimeters which is good for landers and other technologies such as the telegram, telephone and if you want to stretch to some of Tesla’s more theoretical work wireless transmission of energy which could be used as a way of making crafts lighter and smaller. Tesla also created the first radio controlled boat in 1899, this could allow for you to incorporate some kind of probes into your settings and maybe even add live video (if you want to stretch it) due to Edison’s work at the time in phonograph and video technologies, both of which could be incorporated into the telegram/ radio technology to create a live projector feed from another location.
If you are going to lean more on teslapunk this means you can use higher levels of electrical technology such as better lighting and you may even be able to stretch it a bit and use a plasma based form of propulsion as he did invent the plasma globe so the electrified gas would be at your disposal.
if you want to think about power sources, steam could be an option but the main problems come from the storage of the smoke that comes from the engine, as the steam could be cycled back round maybe to help heat some of the interior sections of whatever spaceship/station/base you may need heating, however the smoke can either be stored in some kind of exterior tank or with some effort and time you may be able to recycle some of the components (hydrogen, soulful, oxygen and nitrogen to be used either in the engine or as fuel due to the oxidiser and also hydrogen and nitrogen that occurs in the smoke.
transport around other bodies such as the moon, if you want to keep it realistic, could better be achieved by some kind of powered transport than horses as these eat up your life support and also your food and would be extremely hard to put in a spacesuit and ride around. We have had stem powered cars since1769 but these would only move quite slowly if you want to keep them at a minimal size but gasoline powered cars have been around since 1879 so these would probably be more viable as they are more efficient and also faster. If you are more inclined toward trains, sure they are a workable solution but the smoke problem comes up again, therefore a more efficient method would be the use of a tram like system as non horse drawn trams have been around since 1873.
rocket propulsion is often where people get stuck when it comes to steampunk space travel, if you look up first rocket you will get a variety of dates which can seem confusing but the first true chemical rocket, the type of rocket used for space travel today was made in 1926 which is a bit late but the first real use of rockets was in 1232, this is because they are using solid or powdered based fuels, this is viable but it isn’t the most efficient as once you light it you can’t stop it and there are multiple risks of combustion. There was rocket fuel materials in the 1800s but the scientists had never considered space flight in such a way so if you can conjure a sort of drive for research into space flight you could definitely have somewhat efficient rocketry decades earlier.
With flight calculations you can use rangefinders and other technologies but you still need some pretty advanced maths to be completed to be able to fly a spaceship, Charles Babbage anylitical engine which he worked on in 1838 was intended to be able to complete any calculation set before it, so even if you did incorporate this technology there would still need to be a person aboard with a solid knowledge of astrophysics to be able to handle formula and actually make sense of the calculations.
life support can be a challenge as oxygen is limited, water could be recycled or made through fusing oxygen and hydrogen but air, not just pure oxygen would be a challenge, you can have large areas filled with trees and such if you want to retain o2 and co2 levels but that only works in larger areas. Electrolysis could be harnessed to split water into hydrogen and oxygen as this process has been used since 1800 but this requires power.
Power doesn’t just have to be generated through steam, gasoline was in its early stages at the time but also you can use the method of causing a liquid to boil by heating it due to the sun, this would be easy if on an atmosphere-less body or just in space this expansion of gas can be used to pump a motor creating electricity.
