Shorting any asset is agreeing to sell it at the current price(ish) on a future date. So yes, a bet that it will go down in value. Doing that without having a corresponding right to own the asset is “naked short selling”; doing it with either ownership of the asset or at least the contractual right to own the asset is “covered short selling”. Naked short selling is mostly illegal on many developed markets (including the US, although the wordings around “right to own” are a bit weak).
Either way, no new units of the underlying asset are created, and for every agreed sale of a unit, a purchase of a unit is also agreed (as you say above), so the net difference is zero, every time.
The ones buying the contract don’t own the asset until the strike date. So you don’t have two owners at the same time. One owns the asset, the other owns a contract to buy the asset in future.
When market events turn against market participants (such as during a “short squeeze”, the pressure is on the short sellers, not the underlying asset itself. The short sellers may get wiped out, or go bankrupt, or not be able to pay their debts, but the asset itself is unaffected - the market price of the asset might change, but there is no change to the asset itself, nor any change to how many units of it exist.
There are two types of broker/custodian - fiduciary (sometimes called “full service”) and non-fiduciary.
Full service ones (such as Interactive Brokers) give you the option to allow them to lend/repo your assets in exchange for a cut of the fees they generate, or not - your choice. Customer assets are segregated from company assets.
Non-fiduciary brokers (such as Robinhood) are basically just borrowing your funds, don’t have that separation, can do what they like with your money, and are basically just promising you you’ll get what you expect, as you describe. Best avoided, and not the only option available.
Digitalisation of exchanges makes it easier and quicker to do all of this, but it didn’t herald the start of this - short selling is just a sales purchase agreement, a contract. Contracts have existed for millennia.
Sometimes people sign contracts they then can’t deliver on - this is counterparty risk. It’s part of the free-ish market though, and nothing to do with governments, fiat currency, central banks, etc. The vast majority of trades and contracts are by and between private individuals and companies 🤷♀️