The strength of a coffee brew level is a measure of how noticeable is the flavor in the resulting beverage. Pretty simply, it describes how much of the stuff in the cup is not water. This is why strength is a property of a brew, not a quality determined by the beans.
Strength is directly quantified by the concentration of coffee extract present in the solution. A very diluted coffee is “weak” or watery, while a highly concentrated coffee is said to be “strong”. This concentration can be measured with a digital refractometer and is usually defined by the Total Dissolved Solids (TDS) since soluble solids in the Coffee Extract are the main responsible for the flavor.
The range of acceptable concentrations for each of the Extraction Methods is a matter of personal preference and varies across cultures. Anecdotally, a mildly strong Pour Over by American standards is mildly weak by Brazilian standards.
It’s important to note that the strength of the brew is not necessarily tied to the Extraction Yield of the coffee dose. It’s possible to have weak and bitter (over-extracted) coffee as well as strong but plain (under-extracted) coffee, as depicted in the Brewing Control Chart.
One could argue that suspended solids should impact the measure of strength, given that they end up in the cup and it technically fits the criteria of being not water. This idea is not absurd as suspended solids can contribute to the flavor and interfere with the sensory perception of the brew strength.
On the other hand, an heterogeneous mix is hard to objectively analyze because the solids can easily precipitate. This means that if suspended solids were taken into consideration, the strength of the brew would keep changing over time and place of sampling. It’s more productive to focus on the homogeneous part of the brew to get a single and consistent “strength” measure, hence strength really is more “precisely” described as how much stuff in the water is not water.
This really thorough guide by Mitch from awasteof.coffee on measuring TDS to calculate Extraction Yield.