That’s the point. He doesn’t. No one does.
We do because that’s all we see of the setting - Jedi stories. But the vast majority? Never seen one. Stuff that happened on another planet a long way away.
And then a couple of decades of authoritarian regime to erase the history.
It’s not like there isn’t precedent. And even if you don’t like it, this is how the setting is presented.
Look at Andor. How much do they talk about Jedi?
“Hokey religions” and all that.
It's not that Han doesn't remember Jedi, he doesn't believe in the Force and think Jedi were charlatans: "simple tricks and nonsense". To me that scene is meant more to establish Han's character, rather than a statement on the galaxy at large.
The perspective we get at the beginning of the first movie is very skewed. Han's supposed to be the cynical, no-nonsense shady type, while Luke has been actively denied information on the Jedi by his guardians, for obvious reasons.
After all, in the same movie we see Han's beliefs were not universally shared: at the end of the Death Star attack briefing, the speaker dismisses the pilots with "May the Force be with you". In Rogue One we can hear Rebels invoking the Force blessing a couple of times, and Ackbar does the same in Return. Not to mention the Guardians of the Whills in Rogue One, and Jin remebering that Kyber crystals were used for Jedi's lightsabers.
It makes sense for younger generations not to believe in Jedi/Force with most Jedi being dead, and the Empire actively repressing their mention, and some of the others will actually have bought into the Empire propaganda. After all, there are people who apparently believe Earth is flat or that we never went to the Moon.
But most older people will definitely have a reasonably accurate recollection of the old times; they simply keep quiet because discussing this stuff is at best useless, at worst can get you killed.
Also, you said it yourself. A large part of the population spent a long time hating and fighting the Old Republic because a Bad Jedi killed Uncle Bob, and now what? They just go "Actually, Uncle Bob just fell from a ladder when changing a lightbulb. My bad."?