You can hold a silver spoon in a jug - you are unlikely to get any worse from this. Small amounts of silver ions do not appear to be harmful. But I would not get carried away - by all sorts of ways to increase the amount of silver ions in a solution of water, such as electrolysis, etc. I would also not be fond of uncontrolled intake of drugs based on silver, such as protogol.
There is Argyrosis disease - irreversible changes in skin pigmentation caused by by feeding silver in one way or another into the human body. You can read more in Wikipedia. Once I met such a patient on the street - to look creepy.
for clarity, photos from the Internet were uploaded:
The first thing to consider is whether your spoon is coated with any coating to protect the silver. If the spoon from a long exposure to the air becomes covered with a dark coating (silver sulfide), then most likely the spoon does not have a special coating.
If you polish the spoon well, getting rid of all the silver sulfide formed on its surface, place it in water, then the silver ions Ag +, which just have a disinfecting effect, will slowly go into solution and work to preserve freshness of water. There is evidence that a silver solution is effective when the concentration of silver ions in it is from 0.00025%.
The solubility of metallic silver in water is several orders of magnitude lower than this figure, therefore, in domestic conditions it is unlikely that it will be possible to obtain a solution of the required concentration. In addition, it should be borne in mind that the Ag + cation reacts well with various negatively charged ions found in even clean drinking water. The bound silver ion will no longer kill microorganisms.
It may make sense to store water in a silver vessel, thoroughly cleaning it from plaque before use. In this case, the contact area is larger and the silver will go into solution to a greater extent.
Silver ions quietly dissociate in water (very quietly), have antiseptic properties. I don’t know how large the benefit is, but there will be any benefit.
Upd: I remember that I treated my throat with a certain solution with silver, I helped. In industry, silver is used to purify water (but these are ions. How strongly ions from a spoon can dissociate, I repeat, I will not say).