Chaosmancer
Legend
Every edition that I've played has had listed prices for living expenses and equipment. The rules assume that you are going to be spending most of your money at low levels on room and board, some fresh horses, passage across the river, etc. With all that being equal, different rules had other expectations as well.
In the BECM rules, once you reached a certain level ("name level,") you were expected to spend your gold on a permanent residence like as a ship, or a tower if you were a magic-user, or a castle if you were a fighter. At higher levels, you were expected to become the founder of a small kingdom or settlement, and you'd spend your gold on the armies and siege equipment needed to defend it. CM1, "Test of the Warlords" really focused on this part of the rules, and so did X10, "Red Arrow Black Shield" and the whole "Dawn of the Emperors" boxed set. Ultimately, you would eventually offer your amassed wealth to an Immortal Sponsor and ascend to immortality, but we never got that far (the "I" in BECMI rules.)
In 3rd Edition/Pathfinder, you were expected to spend your gold on magic items and spell components...whether you were buying them or making them yourself. That's it. Magic items became part of character creation in a way...you can Google dozens of build outs for character classes that require certain specific magic items. And sure, rules for purchasing ships and castles were provided in splatbooks later, and rules for armies and mass combat were added later still, but they were all largely ignored and no official adventure modules used them.
In 5th Edition, they tried a more hands-off approach. Magic items aren't specifically intended for sale, but there are scant rules that can be added in if you want them. Later books add more detail for buying and selling magic items, and ships would come later still...but that's it. Seven years in and there are still no rules that I know of for dominions or strongholds, no rules for armies or mass combat, and it doesn't look like they will be getting added anytime soon. (Maybe that's an opportunity? Someone should get a Kickstarter together...)
I will agree that there is little direct support for effectively leveraging your gold.
A lot of the options in the DMG just amounted to ways to waste gold, not to use money to make money. I will second though that Strongholds and Followers does a decent job setting up what you are talking about, and the second book, Kingdoms and Warfare is getting towards the end of play tests and writing, and will be available soon, which gives you actual kingdom management stuff. Nothing nitty-gritty or detailed, but the gaps should be easy enough to fill in if you wanted to.