Are there games that can legally share currencies between them?
Consider 2 games, A and B. In game A, I have 100 gold. I want to move that gold to game B. I have been scouring the internet for such a game; are there any games with at least similar mechanics?
I'm assuming that you mean in-game currency rather than real life money (like US dollars, British pounds, etc.).
Pokemon games have generally included a fairly robust system of inter-game trading, where you can generally transfer Pokemon and items (held by Pokemon being transferred) without restriction between games of the same generation, as well as send some things forward to the next generation.
The main limitation on this is that you cannot transfer money directly, but must send it in the form of in-game items that can be sold in the target game. This is less than ideal, of course, but represents a very old and historical way that real people have transferred their money in the past. Buy jewelry, weapons, fine clothing, etc. before setting sail to a distant land, and then sell it to the locals upon your arrival.
Quite a few people have made charts on what "paths" can be taken when transferring between different Pokemon games. One is available on Reddit.
So, for example, if you are done playing Pokemon Sun, you can take your Sun money and buy some expensive in-game items, transfer them to your shiny new copy of Pokemon Sword or Shield, and then take your Sword or Shield character to the NPC Poke Mart merchant to sell the items for currency in the new game.
The exact mechanics of transfer have changed over the years. In the 1990's, physical link cables between consoles were used. Later, infrared gizmos were introduced where you could dispatch your stuff across the
roomvoid wirelessly. Nowadays, there are cloud apps (Pokemon Bank and Pokemon Home) where Pokemon and items live while they are in transfer. Regardless of the exact method used, this is absolutely one of the things that Pokemon main series games support.