C# find JSON value based only on Key name through multiple levels of array

You can parse your JSON to a JToken, then use SelectToken with the recursive descent JsonPath operator .. to get the terminalSize anywhere in the JSON:

var terminalSize = (double?) JToken.Parse(json).SelectToken("$..terminalSize");

Fiddle: https://dotnetfiddle.net/5ziYbP

If there might be multiple terminalSize keys in the JSON, for example if you had an array of terminals, you can use SelectTokens instead and put the terminal sizes into a Dictionary keyed by path:

var sizes = JToken.Parse(json4)
                  .SelectTokens("$..terminalSize")
                  .ToDictionary(t => t.Path, t => (double)t);

Fiddle: https://dotnetfiddle.net/ivSM88

You may parse your JSON into JObject, then recursively go through all properties and sub objects to find a terminalSize value. There is no need to deserialize the entire JSON into specific object

var json = JObject.Parse(jsonString);
var result = GetTerminalSize(json);

double GetTerminalSize(JObject input)
{
    foreach (var property in input.Properties())
    {
        if (property.Name == "terminalSize")
            return property.Value.Value<double>();

        if (property.Value.Type == JTokenType.Object)
            return GetTerminalSize((JObject) property.Value);

        //not sure, if the is a need to handle an array
        if (property.Value.Type == JTokenType.Array)
            foreach (var item in (JArray) property.Value)
                return GetTerminalSize((JObject) item);
    }

    return 0;
}

It returns a correct value for all 3 examples