As I understand it, nothing has conclusively linked to Solomon that has been discovered in the archaeological record.
But, from what we can tell from archaeology, during Saul’s reign, the tribes of Israel were still living a fairly pastoral life without kings - just shaman/prophets - and where each other valley was its own tribe. There were no palaces, shared temples, etc. it was probably all mostly houses and farmland.
Solomon is only two generations later. Saul unified the tribes under a military leadership, David continued that process, and by Solomon’s time - in my read - the kingdom was trying to achieve recognition from other nations so Solomon was pretty active in trying to make the place look respectable, send gifts to other nations, send diplomats to collect gifts from those nations, etc.
Given that, following Solomon’s death, half the kingdom split off and Egypt eventually came in and plundered the place, my suspicion would be that Solomon was pretty overbearing and really put the screws to his subjects, forcing them to build and mine for gold.
From the Egyptian invasion, we can presume that he gathered enough gold that it was worth stealing.
But we can probably also assume that there was a fair amount of exaggeration in the later descriptions of that treasure.
Given that we don’t live in a gold economy, I couldn’t say what quantity of gold would be a reasonable range to expect - a kilogram, 1000 kg, or what - but my feeling would be that it would probably be far less impressive than any read of the Bible would prepare us for. But it would need to be a healthy little chunk.
At the same time, as said, we’re only two generations off from everyone being sheep farmers. Whatever jewelry and structures they were creating were probably not terribly advanced. Solomon’s “palace” might have been something like a building with multiple whole rooms (ooh, fancy) the size of your average large motorhome more than it might have been anything like what we would envision a kingly palace to look like. On the other hand, in modern times dictators have forced their people to accomplish amazing things in terms of rapidly advancing their technology and the outside appearance of their central, governmental structures. It would really be hard to guess what to expect.