Imagine you lived on an Earth where orbital rings and towers give access to space, the outer planets have been transformed into supramundane worlds, and the Sun is encompassed by a Dyson Swarm. What would the night sky look like?
For megastructures and artificial habitats, just imagine seeing the ISS as it is now orbiting overhead, but multiplied across the entire sky and in many different shapes and apparent magnitudes. Orbital rings and space-elevator structures would resemble bright, shining beams of light arcing across the sky. Mega-planets would probably look like any other planet visible to the naked eye, unless their overall size was significantly increased. If the latter is true, then perhaps you could make out some details on their surfaces if their albedo is not so high. This is all assuming that the engineers do not make efforts to reduce the reflectivity of these structures, perhaps even to the point where some are invisible to the naked eye (i.e. a perfect blackbody object).
Orbital/Lagrange/Statite mirrors will probably reflect sunlight in many interesting ways, including onto the nightside of a planet if required, or on specific objects in space. It is unlikely that the sun itself would dim much from a vantage on Earth when it is surrounded by a Dyson Swarm - unless the Swarm is REALLY thick or some crazy megastructure is orbiting the star and has enough surface area to significantly cover a portion of Sol's face. Our sun certainly will be dimmer (or even invisible) in certain wavelengths at this time though, as some forms of light the mega-engineerers might find useful for any number of technological tasks like photosynthesis or solarcells.
Given the reflecting surface area of an orbital ring, it would seem to me that it would be like a permanent full moon on Earth's night time surface.
Jupiter has an albedo of 52 percent, while Earth's is 30. If you built a shell around it with atmosphere, land masses, oceans and enough focused sunlight to approximate Earth, it would be something like three times brighter and it's already a tremendously bright object.
If you built your Dyson Swarm inside Earth's orbit, how would you keep it from shading out Earth? If you built it outside, wouldn't it blot out most of the stars?
This really depends on the reflectivity of the material these structures are made of. If they are manufactured from a material with very low albedo OR were coated in a highly absorptive layer (which would be the case if they were solar-cells), then absolute magnitude could be significantly reduced.
In plain terms, if there is a relatively low density of objects orbiting the Sun, then our star's overall luminosity will outshine the shading of those disruptive objects, rendering them invisible against the glare of Sol. As more and more objects are placed in orbit between the Sun and an observer, then certain wavelengths will be cut into until there are so many orbiting objects that the Sun disappears. I won't do the math here, but it would take many millions of sizable objects orbiting our star to completely dim it from an Earth perspective. Furthermore, I wouldn't worry about the Earth being completely shrouded in darkness from spatial infrastructure, because orbital mirrors reflecting light where it is needed would be a ready solution.
A similar scenario would play out here. Depending on the distance of the objects from Earth, even objects that are many hundreds or thousands of km in size would disappear among a backdrop of stars, at a rate inverse to their proportional distance from Earth and Sol. Most would be invisible but for their reflective surfaces, if they have any. These farther objects would form many new artificial constellations, and I'm sure amateur astronomers would love seeking out and observing these new nightsky objects.
It would need to be a very thick Dyson Swarm indeed to block out all starlight. Artificial structures that orbit closer then Mars I could see as posing a more immediate concern to our nightsky visibility, but perhaps clever use of orbital mirrors or artificial-skies projected by satellites can remedy that. By the time such megastructures reach this level of pervasiveness in our solar-system, Earth itself may be a Shell-world of some sort, so the ceiling of each layer where people live could support a fully accurate artificial sky.
The solar system has a zodiacal light. If astronomical seeing is good where you live you can see the zodiacal light before sunrise and after sunset. The energy emission corresponds roughly to a K1.3 civilization. Up to K1.2 in the solar system there will not be any visible change. At K1.4 it would not be noticeable to most people without someone pointing to it. Also the Dyson swarm will be adsorbing sunlight. The natural dust particles should have a different albedo. If the swarm used a polar orbit the zodiacal light would look very different. I am not sure why a K1.3 civilization would do that. The opposite may be more likely. The swarm will show up as a denser line along the ecliptic. There may also be feint rings around Venus and Mercury.
A Kardeshev 1.3 civilizations would use around 1 million times the energy consumed by humans today.
There is also currently a gegenschein in the opposite direction from the Sun. It is harder to see. You would get something like the gegenshien at Earth-Moon Lagrange 3, 4 and 5. The natural gegenschein is at Sun-Earth Lagrange 2, These are much closer to Earth and should show up while civilization is still "small".
The largest disruptions will be in low Earth orbit. If there is no regulation to prevent it there will be advertisements flying overhead near sunrise and sunset. In Summertime a banner in LEO could shine most of the night. The adds might be focused at cities. North-South orbital ring systems will be very bright after sunset or before sunrise if you are looking away from the Sun. Space elevators will be in sunlight for most of the night. The station will be at a fixed location and should resemble a star. The cable would be a feint line for part of the night. The cable will seam to fade in the direction of the station.