When would one carry a sword on a shoulder with grip upwards?

Whenever the sword is too large to carry on the hip, and usually when you are marching towards the battlefield.

Swords, despite their prominent role in fiction, and in real life as a status symbol, were almost always just a sidearm on the battlefield. The primary melee weapons on the battlefield have been the polearms, used in close formations.

Swords which were not too big to be able to be carried in a scabbard on the hip, on the battlefield were a secondary weapon in case your main one got damaged (or you were an archer and found yourself in close combat). However, in peacetime, people carried swords with them for self-defense, because they were easy to carry without getting in the way. You wouldn't go grocery shopping with a pike three times as long you are tall, you carried a sword on your hip, just like today the preferred firearm to carry around in time is a pistol, not a machinegun.

However, there were a few cases of swords being used on the battlefield in a more prominent role. But unless you were engaged in combat, it was not a weapon you had to draw at a moment's notice, it was part of your equipment which you carried on the baggage train or on your shoulder, like you would carry a pike. Most of a military campaign was spent marching and not even near any battlefield.

Historically, scabbards were very rarely if ever worn on the back.

Here is a pretty useful and well-researched video about carrying swords which are too big to fit in a hip scabbard: https://www.youtube.com/watch?v=vQBfNoi28Z4

As a veteran who has put some miles on his boots. I would say that this is a way to carry any heavy weapon with less stress on the body. Putting heavy weapons on your shoulder is easier than hand carry or slung on your shoulder with a sling, with the rifle pulling the weight down with a lower center of gravity. Same if you attached the weight to your hip. You can still slide your weapon down and arm yourself quickly. In fact, just as quickly as you can with it slung by a strap. So I would say this modern explanation easily crosses over to antiquity, with your sword question.

I made a jokey comment in the question comments, but this is in fact something that was done.

There were apparently two techniques in medieval German swordfighting that involved grabbing the blade. The first is called half-swording, and involves grabbing the sword halfway up the blade with the off hand to get more point control and leverage on a thrust. The idea is that this is more likely to pierce heavy armor plating.

Below is an illustration of this from an early 15th century manuscript.

The second was called the mordhau (or murder stroke¹), and involved using the blade as a handle and striking with the pommel or guard, effectively using the sword as an impromptu bludgeoning weapon (role-playing GM's take note).

Below is another picture from a 15th century German martial arts book that demonstrates both techniques in use.

There's a pretty good youtube video from a historical martial arts fan displaying the use of both techniques. That might be helpful for visualizing the physics of how/why this worked.

For the examples given in the question, the first shot looks very much like an armored fighter looking to deliver a murder stroke. The second one looks more like an armed guard facing a crowd while holding his sheathed sword in a position where it would be pretty easy to use as a club in a similar manner. In this case nobody in the crowd looks armored, but this might be a subtle message that while not interested in spilling lots of blood, the wielder isn't above bashing in a few skulls should the need arise².

So score one point for the historical research of videographers for Polish Pop Princesses.

^{1 - Definitely the name of my next RPG superhero character.}

^{2- If you are inclined to be generous to the actor and director}

This is anecdotal, but enough people seemed to like my comment and OP had further questions, so I'm posting it anyway.

I did some re-enactment in my time. My weapon of choice was a longsword. (Well, a bow actually, but I digress..) Carrying that sword at the hip was inconvenient due to its length (a bit over four foot, pommel to tip). And once drawn, the scabbard (now decidedly unbalanced toward the back) tended to get in the way.

Carrying it on my back was also inconvenient (e.g. if you wanted to sit somewhere), and there was no way you could draw it from there, or even unsling it, with any kind of speed.

So most of the time I carried the sword, sheathed, either with my off-hand at my side (grip forward for quick access), or -- especially when things got crowded -- pretty much exactly as pictured here: held by the tip, with the grip up over my shoulder. Actually, you don't so much hold the sword, you just counterbalance it a bit. The center of mass is on or even over your shoulder, so there is not much holding required -- in the picture below, my hand is casually resting on top of the scabbard.

If you hold the by the grip, all the weight is in your hand, and the tip just leans against your shoulder -- if that much. Someone bumps into you, that tip might go any which way. And when I turned the sword grip-down to take that picture, it almost slipped from my hand and out of the scabbard, further proving my point. ;-)

For "combat", I would draw the blade and just put the scabbard away, so it would not hinder my movement while "fighting". When sitting down, I would just lean it against the wall beside me.

Carrying it by the tip also sends a clear message: "Just coming through. Yes, I am carrying a sword, but I have no intention to draw it on you just now. As you were." It also lets the people see what a really nice sword you have there. ;-)

All the above, by the way, carried over 1:1 to LARP. A hip scabbard is nice for overland travel or on horseback, but indoors I much preferred just holding the scabbard in my hand. And people are a lot less touchy when they see a couple of feet between your hand and the sword hilt.