Does it matter to my price if my competitors are also quietly for sale right now?

It can, mainly through its effect on buyer choice rather than any change to your business itself. If serious buyers know, or come to learn, that several similar businesses are available around the same time, they have more options to compare and less urgency to meet your specific asking price, since a comparable business down the street might offer similar value on different terms.

The nuance is that this dynamic is often invisible to sellers, since competitors exploring a sale quietly rarely announce it, and you may not know your business is being compared to others until a buyer mentions it, or simply walks away toward a different opportunity without explaining why. It's one of several reasons a controlled, well-prepared process, rather than an open, drawn-out one, tends to serve sellers better in a market with multiple similar businesses potentially available.

Because you generally can't control whether competitors are also exploring a sale, the more useful response is making sure your own business stands out on the things you can control: clean financials, reduced owner dependency, and a clear, well-supported price. A business lawyer and broker together can help you present your business competitively regardless of what else may be quietly on the market.