And medieval people definitely built monuments to themselves. A great example is Battle Abbey [0]. The official reason it was built was as penance for William the conqueror killing so many English, but there is definitely a strong case to be made that building such a grand abbey was in 0art to signify the new Norman rule and to remind people of who was in charge. They weren't venerating the architect, but it was very clear to everyone who paid for the abbey and William remained very much linked to the structure. That would have been one of the most impressive buildings for a very large area, even it's ruins remain impressive nearly a millennium later. It's a religious building, but it was even at the time very much linked to a secular ruler (inasmuch as the rulers of the time were secular).
The legend say that when the king tried to flee the revolution he was only recognized due to a coin with its face engraved in it. A teacher taught me this one with a variant where the king itself gave the coin to pay in a tavern. Now even it is just a legend, that also gives an interesting reflection on what it means to be famous at this time.
https://www.numismatique-en-maconnais.fr/2018/04/larrestatio...
Not many people realise that the more distant locations in Shakespeare's plays were close to science fiction. If you were a British peasant visiting "Verona" or "Venice" was like visiting the ISS. You might get swept up to fight in France, and there was a tiny chance of joining the navy. But most people spent most of their lives within a tiny area, with little idea of what was happening elsewhere.
So cathedrals were stunning. If you somehow visited a cathedral city you'd be struck dumb by the size - unimaginable to someone who grew up on a small holding.
If would likely be even frillier, more colourful, and more organic if Gaudi had seen it all the way through.
It's still one of the modern wonders of the world.
The Washington Monument in DC, for example, famously is different colors because they had to change the source of marble during construction when funding halted for a time.
Fiction, but you if wonder about things like this, you might be interested in The Pillars Of The Earth series about the building of a cathedral in 12th century England.