I want to make it clear from the outset that any OSR style game, or games with gold for XP, should absolutely not use this system under any circumstance. This concept is more fitting for a generic adventure or high fantasy story game. The granularity and importance of keeping track of individual gold pieces and time is not necessarily something you want for a more casual game; so this method is a compromise between more objective systems and the more abstract wealth-as-a-stat system found in some games.
In some PbtA games, wealth is like an abstract stat. The idea being that anything under your wealth level is not something you need be concerned with; but anything equal to or over your wealth level is a significant purchase and will or has a chance to reduce your wealth level by one degree. The idea behind this system is to more accurately portray a character's lifestyle within the world; a high class noble has no concern over daily lodgings and meals, and can freely buy horses or servants if needed without any impact to their overall finances, but buying a powerful magic spell or a castle would be something they need to carefully consider. On the flipside, a character with a wealth level of one or zero would have to carefully consider how they will make enough money each day to afford their meals or simple services.
The idea is to take the above basic system, but instead of abstract stats or levels, tie your wealth level to each significant treasure you have looted.
Wealth as Treasures
As adventurers explore the world, do quests, and raid tombs, they will eventually come into possession of valuable artifacts. Some of these may be magical or very powerful; as as such will be valuable, but some will be valuable purely for other reasons; great works of art and craft, huge gemstones or precious metals, cultural and historical significant, etc. These are your treasures.
You are only going to be keeping track of significant treasures; typically the namesake of whatever dungeon, tomb, or royal family you're stealing from. If your players make a plan to steal the Mona Lisa, then that would become the significant treasure written on their character sheet. The other paintings and valuables in the Louvre that were stolen fetched you a lot of money, but those are part of the abstraction. Naturally a thief or graverobber will keep the best finds for themselves- so for each of these great treasures you possess, you treat this as one "wealth level".
Your daily expenses are not being paid by these treasures, you are buying your food and servants with the silver coins you looted from the orcs you fought in the dungeon, or you are making a small daily stipend from the local banking guild by stowing your treasure in their vault- but the treasures remains your primary wealth. When you need to purchase something valuable to your wealth-level, you will need to exchange a treasure for it. The DM decides which treasure you are trading away, not you.
So for example; a character with a single treasure; a glorious golden signet ring from an ancient dynasty, will have enough wealth laying around from their previous dungeon haul to buy their daily necessities. But if they suddenly need to buy a good fast horse to get out of town, they will begrudgingly give away this ring, vastly overpaying, to the stablemaster for his finest steed. Now, when you reach the next town over, you will have lost one level of wealth and are struggling, on the run and hungry, until you can find another valuable treasure to add to your character sheet.
Treasures also scale upwards; while the first great treasure you find may be one piece of jewelry or animate portrait, later treasures will be exponentially bigger and more valuable. This is tied together inherently with character progression; more dangerous dungeons have better treasures, so what counts as a "significant treasure" may change based on how many you already have. You can dive into the lagoon and pry open as many giant clams as you wish for pearls; but one or two or a dozen more isn't going to bring you to the heights of wealth and luxury; you'd need something greater.
Once a character has four, five, or six significant treasures; they'll be living like a King and have no issue affording property, income generating businesses, paying servants, and hiring mercenary bands. But if you want a truly exorbitant purchase, like the construction of a new castle, you'll still need to give up one of your precious treasures for it. While your character's liquid wealth has not actually decreased sans one treasure, consider it like losing a bit of the renown and respect they garnered that helped them keep their level of income before; while the local archbishop may be irritated that you won't donate the lost scrolls of the saint to the church; if you lose them again he'd be downright furious, and stop sending rookie healer-priests to your fort for free heals- thus increasing your expenses. Or maybe, you can't get as much money from pilgrims or wealthy nobles on tour who want to see your collection. You get the idea.