So this is what I’m looking for: a non-renewable item, with a finite amount of it in the whole world, unlike ores. Thanks for the help!
I'm pretty sure what you seek does not exist in vanilla survival minecraft.
Without glitches only one Dragon egg can be obtained in the whole world. Technically one is a finite amount but practically it's not very useful as currency.
Similarly technically Minecraft has a world border, so eventually you will run out of new chunks to search to search for structures and ores, in practice you will run out of disk space on your server long before that happens, so they can't really be considered finite in a meaningful sense.
There really are only two structures in the Minecraft world that are "finite" in the way you desire. The strongholds in the Overworld and the End fight arena in the End. Other than the aforementioned dragon egg neither of them has any unique items.
In Java Edition, written books can be used as a form of currency if the player who creates them is trusted, as they are marked with the name of the player that created them and while copies and copies of copies can be made, they are identified as such and copies of copies of copies can't be made without glitches. So if the creating player keeps close control of the originals and copies and only lets copies of copies be distributed then they can limit supply. According to the Wiki though in bedrock players can customize the signature line, so I think this may not work as desired on bedrock.
If you are prepared to let a server admin use cheats/commands to create your currency then you have more options. There are many items that can only be introduced to the world via commands and hence an admin can introduce a limited supply of them. This can also sometimes be used to create otherwise-unobtainable variants of normal items, for example the aforementioned written books have a "tattered" option which is only accessible through commands. There is the question of how to handle initial distribution to players though.
Finally be aware that duplication glitches are frequently discovered in minecraft (the glitches in Java and Bedrock are different but glitches are found in both), so even if you have admins create otherwise unobtainable items there is still the possibility that someone will duplicate them.