Tradition can not be forced.
In most stories and games, many traditions are unheard of and unheard of. Tolkien had whole continents that shaped the world of Lord of the Rings, but if the effects of history were seen, the stories themselves were not (the ancestors of Aragorn were originally attracted to Middle-earth by Morgoth, the first lord of Mordor, who created the balrogs!) Skyrim had entire libraries of books and dialogues on the dwemer, but most of the players having played the game the ignored. Dark Souls and Bloodborne have one of the most in-depth narratives, but they are so fragmented and hidden in various elemental texts and dialogues that whole communities must work to decode everything, and most do not disturb.
Ensuring that people care enough about reading traditions is one of the biggest challenges that a world builder can face.
So, how can I make people anxious?
Now you can get into the psychology of the game and its motivations, but the simple answer is "Link your traditions to what interests your players".
With DnD, the best way to do this is in the three things that make DM crazy. Objects of hoarding, assassinations, and players in the spotlight. Old or new players, players have fun with cool objects and battles and have the opportunity to show their characters.
If you want your players to care enough about reading books, you may want to consider casting some pretty glaring clues. You find a broken sword that seems to emit a sacred and unholy energy, and an identification spell reveals that, if it is corrected, the sword of this "ashtray gods' tailor" is super powerful. Now, the terms "Ashkeeper" and "Godslayer" are linked to a booty potential.
Now, they can read a page about ashtrays, but a complete book may still be too much. Now, they are facing a horde of undead with unusual abilities, like zombies with real vision and inflicting holy and unholy damage, and they are zombies of ash guardians, and the symbol of them is everywhere on their clothes. Suddenly, learning more about ashtrays could not only give a fresh sword, but also relate to the truth, and perhaps even to super zombies.
Finally, examine the weaving of ashtrays in the background of a character. One of your player's characters may have a coat of arms and the ash seller symbol appears in his coat of arms. Now, players can have their character as star of the week if they can push the guardians of ashes into a central role.
And, in doing so, you can create an interest in the tradition and start sharing the tradition. According to what I wrote, you know that ashtrays exert sacred and ungodly powers, that they were formal enough to influence the family's coat of arms, that they use swords enchanted and that they are turned into zombies with extra powers. From here you can build the tradition.
The best way to know if a party is ready to make itself known is to start actively seeking it. If they start looking in libraries for books bearing the symbols of the guardian of ashes, or go to a bookstore in a city in search of guardians of ashes, or will show the broken sword and ask questions to About the guardians of ashes.
What should I avoid?
In many games, I've heard of an obstacle called "paper fatigue". Players must constantly check their sheets and scan them to look for scores and skill modifiers, skills, feats, features, attack bonuses, and so on. It's a lot of text, a lot of scanning, and it can be very frustrating and exhausting to leave. through workbooks whenever you need to find a number. Adding more paper to this situation can be the straw that breaks the camel's might, and you risk losing the party's investment and immersion.
Also, avoid the railways. If the party does not want to read the traditions, do not punish them for that. If your players are more interested in the story than in the exploration of the story, do not punish them for it. You may need to find another part.