Do options deal with overhead supply in a similar way stocks do?

There are two points to the answer. Options are derivatives, meaning they derive their value from the underlying security. Thus their value in the most general sense is tied to the movement of the underlying security. There are other factors that come into play such as volatility, time until expiration, the security price in relation to the option strike price, but a strong price move one direction or the other drives the option value.

Thus, overhead supply that impacts the movement of the underlying security, i.e. a prior price peak over the past few months, can stall the stock’s move and thus impact the option’s price. If you own a call option (rises when the stock rises), a stall in the stock price stalls the option price and even reduces its value as volatility drops. If it is closer to expiration, it loses time value as well.

A second consideration applies to the option itself and the number of open interests at particular strike prices. As expiration approaches, a stock tends to gravitate toward the level with the most open interests. If the market is slow, the stock typically will close just the other side of where the highest open interests reside. In other words, say there is a high open interest in $40 call options on a stock that is trading at $38 and not moving much. As expiration approaches the stock will tend to cheat toward $40, but it will also often fail to surpass that level. There is an old saying that in a slow market, at expiration a stock will close at the level of the most pain. In other words, the above stock would close below $40 and those open interests would expire worthless.