The planet’s polar axis will be oriented relative to the fixed stars. It cannot point to the Sun year round.
That doesn’t mean you can’t have a planet with a permanent hot & cold side. That just requires the planet’s polar axis to be oriented normally, i.e. roughly perpendicular to the orbital plane, and have the rotation & revolution rates be the same, or very nearly so. IOW, like the relationship between Earth & Moon.
Back to Uranus …
If we assume the polar axis is exactly in the orbital plane and tangent to the orbital curve at the day we define to be “the first day of the year”, then we get some interesting day/night behavior. Let’s also assume, like Earth, that the rotation period is short compared to the orbital period (i.e. 365 to 1). Let’s define North as the direction of the Pole that faces into the orbital motion. We’ll assume the rotation direction is towards the East, like on Earth.
We’ll have to be careful with terminology here. I’ll use “day”, night, noon, midnight, dusk, dawn, etc, to refer to light/dark and the apparent position of the Sun in the sky, and “rotation”, “rotation period”, orbit, orbital period, etc., to refer to the actual physical motion or time intervals.
In that case at the first of the year, people at the Pole will experience the Sun on the horizon, and over one rotation the Sun will make a full circle of the horizon. It’ll be perpetual dusk/dawn throughout that rotation. This is the same experience as someone on Earth right on the Arctic Circle on the solstice day.
On the first day of the year, people on the Equator will experience something like a normal rotation on earth. the Sun will rise due East, traverse the sky to Noon in 1/4 a rotation period, then set in the West after 1/2 a rotation period. Then it’ll be dark for 1/2 a rotation & the stars will move from east to west like the Sun did. This is the same experience as someone on Earth right at the Tropic of cancer/Capricorn circle on the solstice day.
So far, so normal.
Let’s fast forward 1/4 of an orbit, i.e. one season later. People at the Poles will be in perpetual sunlight or perpetual darkness. For the South Pole, the Sun ill be riveted directly overhead & just hang there. For the North Pole, the stars will rotate in a circle once rotation period, but the circle will have a fixed center, at least for a few days.
Someone on the Equator will see the Sun on the horizon due south. It’ll just hang there. Just North of the Equator will see perpetual twilight, and further north perpetual darkness. Just south of the Equator will be perpetual dawn, with the Sun a few degrees above the horizon due south. The further south you go the further above the southern horizon the Sun will be. By the time you get to the south Pole, the Sun will be directly overhead, perpetual noon. The Southern sky will be rotating once every rotation period, just like the Northern sky does, but you won’t be able to tell that since there’s nothing to see in the sky except the apparently fixed Sun.
1/4 orbit later, we’re back to the same scenario as at the start of the year. Perpetual twilight at the poles and normal Earth conditions at the Equator.
And 1/4th orbit after that, we’re again doing the perpetual light / dark at poles and perpetual twilight at the Equator. The Poles will have switched roles, perpetual noon at the North and perpetual dark at the South.
The intermediate points 45 degrees between the 4 compass points on the orbit I described are fascinating. As is the whole flow of the year. Very hard to put into words, so I won’t try a comprehensive explanation.
Just as an example consider the South Pole on the 1/4 orbit day, where the Sun is frozen at the high Noon (straight up = “zenith”) for a whole rotation. On the next rotation, the Sun describes a small circle around straight up. It may be small enough that the Sun appears to wobble, where the center of the circle is inside the disk of the Sun. The next day the circle is wider, and wider and wider.
The Sun appears to be spiraling away from the zenith, taking one rotation period to make a trip around the ever-growing spiral. Eventually the spiral gets so big that the Sun is 45 degrees between zenith and horizon, moving from easterly all round the horizon but always at 45 degrees. By the time we cover ¼ orbit, the spiral has spiraled out to the very horizon and the Sun skims the horizon for a complete rotation.
Then it sets, spiraling down towards nadir, the point directly beneath our feet. For the next 1/2 of an orbit we won’t see the Sun. We’ll just see slowly deepening twilight followed by darkness for another 40%-ish of the orbit. Finally there will be a slow dawn & the Sun will reappear to make a skim around the horizon in one rotation period and begin its spiral to zenith again. When it gets to zenith, the year will be over.
The experience of a year on the Equator is equally weird, but not at all the same as the experience at the poles. I can’t even begin to describe what a year looks like from a point at mid-latitudes.
Truly not like what we’re used to.