If movies are anywhere close to accurate. For centuries almost every country had armies with thousands of men who all had swords, armor, shields, axes, hammers, Morningstars, etc. For the whole world that seems like once guns became widely used that would leave millions of of handheld weapons. What happened to all of them?
Rusted, recycled, buried, or in rivers/lakes/seas.
Sometimes, swords were used until broken or worn out (e.g., from too many resharpenings to remove nicks from the blade). Pre-modern steel was valuable enough to recycle - don't leave it in a garbage pile to be found by us today, but recycle the steel instead. (For bronze, also recycle.)
Swords that were obsolete (e.g., in modern times, a military model of sword that was withdrawn from use) could be sold, given as military aid, or converted to training weapons (many of the surviving P1885 British cavalry swords have rounded blunt points from use as training weapons). Or sold as scrap for recycling.
Swords that were no longer needed as swords were sometimes used as tools (or modified for use as tools), until worn out or broken.
Swords were sometimes buried with their owners. Depending on the soil conditions, many rusted, and some survived and are occasionally found today.
Some were preserved as relics, mementos, trophies, etc.
Some were sacrificed by being thrown into rivers, lakes, bogs. Some of those survived, and are occasionally found today.
Some were lost.
Some were deliberately destroyed. In some cases, this was by being buried, or by being thrown into the sea.
Some were hidden.
Through those different paths, the end results were often similar after a few hundred years: rust or recycling. 20th and 19th century swords are still common, 18th century swords less so, and progressively older swords become more rare. Bronze swords have survived better relative to iron and steel swords, since they are much more corrosion resistant.
Bronze pommels and guards are sometimes found by themselves. In many cases, they would have been lost/buried as part of a complete sword or knife/dagger. The iron/steel rusts away, leaving the copper alloy parts. An example of an isolated pommel find: https://finds.org.uk/database/artefacts/record/id/470331 Jade scabbard slides (and jade pommels and sword guards) are also found without their swords/scabbards - jade survives where steel and wood do not.
An example of a buried cache of weapons. Note the severe rust, after less than a century: https://www.stripes.com/news/pacific/workers-uncover-cache-of-wwii-firearms-swords-at-tokyo-elementary-school-1.541347
On the destruction of Japanese weapons at the end of WW2: https://history.army.mil/books/wwii/MacArthur%20Reports/MacArthur%20V1%20Sup/ch5.htm (note the photos of weapons being dumped at sea - in this case, not swords, but swords suffered the same fate). There were earlier deliberate destructions of Japanese swords, the most famous being Hideyoshi's sword hunt of 1588 which removed many thousands of swords from circulation.
Well, they stuck around for a while, but keeping in mind that guns have been "The thing" for several hundred years now.
Most parts of most weapons are very biodegradable. Wooden handles. Cloth and leather wraps.
The only parts we should realistically expect to see from the medieval earlier periods are steel and bronze parts that have been preserved some how. Typically, at least in western Europe, from burial sites and battlefields as well as a few preserved in private collections.
And lo and behold:
https://www.britishmuseum.org/
https://www.wallacecollection.org/
For just a start.
There are also several European collections of military arms armor in government "Royal Armories".
And then of course you have the private antique dealers that have lots of them for sale. Particularly 18th and 19th century examples. But, some older stuff creeps in occasionally.
For example:
A surprising amount of that stuff is still around, but since it is no longer being produced wholesale for military use, it fades away with time.