Can selling naked calls create counterfeit shares?

AFAIK a fixed amount of call/put contracts is not "issued" by anybody the same way that a company decides to issue shares and dilute its own holding.

That is correct. There's is no limit to the number of options that can be created as long as you have the required margin to support the naked short option position. However, brokers tend to raise the margin requirement in situations like GameStop.

Call contracts come into existence and get destroyed dynamically whenever a buyer and a seller agree on a strike, expiration, and premium.

Yes and no. Contracts come into existence when both parties take opening positions. Contracts are terminated (destroyed) when both parties take closing positions. If one party is opening and the other is closing then contracts are just changing hands. What's germane to your question is that the selling of the call increases open interest thereby affecting the option market maker's need to add long delta (buy shares) in order to remain hedged.

Theoretically if an option seller decides to sell a lot of OTM naked call contracts (without delta hedging), the stock price goes up, buyers of the call options decide to exercise, does that lead to FTDs?

Assignment of a short call results in a short position in the underlying. In and of itself that doesn't create the FTD. FTD is a conscious decision by the trader not to borrow the stock, resulting in a naked short (equity). It's no different than naked shorting of the stock without acquisition of shares for delivery (FTD).

What market mechanisms exist to prevent this?

The broker is supposed to borrow shares for the newly opened short equity position and close it down if borrowable shares are not available. Evidently, it's not a foolproof system since there are frequent complaints about the illegal practice of naked shorting of equities.

To sell a naked call, you need to have margin, and a lot of it.
To get in an area of even 50% of the stocks, you need to have a significant chunk of money, far out of reach for normal investors.