Even in dollar terms it actually did go down.
https://www.macrotrends.net/countries/USA/united-states/mili...
Late 1989 was the fall of the Berlin Wall and the end of communism in most of Eastern Europe and 1991 was the end of the Soviet Union itself. There’s a drop between 1990 and 1991, a slight increase in 1992 (replenishment after Desert Storm?) and then a gradual decline in nominal dollars throughout the 1990’s. Also remember that federal budgets were usually passed ahead of time; this was before the government normalized all the government shutdowns and other monkeyshines we have grown accustomed to today, so budget changes might be a year behind current events. Adjusting for inflation the drop in spending would be even more.
Spending does start to increase after 1998. I’m not exactly sure why, but a lot of things started happening in 1998 and 1999, ranging from Bin Laden’s attacks on American embassies, the Kosovo conflict, Saddam Hussein ejecting UN weapons inspectors from Iraq, the discovery of Chinese interference in the 1996 elections and China stealing nuclear secrets.
Also, at the end of the Cold War, there were a number of systems that were in the late stages of design and development that were either radically cut back or canceled outright. These included the F-22, B-2, and Seawolf class submarine, just to name a few big ticket items. This saved a lot of money and made sense at the time since these were all designed specifically for Cold War missions that no longer seemed relevant. But eventually the older hardware still needs to be replaced; instead of replacing the Los Angeles class submarines with the Seawolf class starting in the 90’s, you end up replacing them with the Virginia class starting in the 00’s.
Other cutbacks during the post-Cold War period included closing military bases (which was fraught with political difficulty; no congressman wants the base in his district to be closed!) and reducing the number of US forces permanently stationed in countries like Germany.
Dollars aren’t the only measure, either. One of Reagan’s goals was a 600 ship navy. It takes time to build ships so it wasn’t until 1987 that the US Navy reached a peak size of 594 ships. Currently the US Navy has 238 ships. Sometimes a higher defense budget means you’re building a larger military but sometimes it means health care has gotten more expensive or you need to buy more fuel and ammunition to support operations. This also explains the drop after Korea.