No, socialization of the economy is not the only metric. It is not even the key metric. The class character of the state is primary. Socialization is a single, highly important factor within that determination, but it remains derivative. A nationalized industry under bourgeois state command functions as state monopoly capital.
Evaluation proceeds from the principal contradiction to its secondary aspects. The principal question: which class holds monopoly over political power and the means of coercion? This determines the direction of all other processes. Secondary metrics, the rate and depth of socialization, the trajectory of productive forces, the composition of administrative personnel, the character of ideological struggle, these are not irrelevant. They are conditional. They either consolidate proletarian state power or undermine it. There is no neutral technical criterion. The same policy, e.g. grain procurement or industrial planning, produces opposite class effects depending on which class commands the state apparatus.
The state is not a passive vessel for economic measures. It is the organized expression of class rule. Transitionary societies contain multiple modes of production in contradiction. The state resolves which mode dominates. Empirical assessment must therefore begin with the class basis of political power.
No the petty bourgeoisie often do hire workers to supplement their own labour. The bourgeoisie own the major means of production and live by extracting surplus value from wage labor, they do not need to work themselves. Petty bourgeoisie own small-scale means of production (a shop, a workshop, a plot of land) and still rely on their own labor, however often employing workers to supplement their labour.
In periods of socialist momentum, the petty bourgeoisie frequently become the most zealous allies of reaction because their precarious ownership of small-scale means of production places them in direct fear of expropriation and descent into the proletariat. Unlike the bourgeoisie, who may calculate accommodation with a rising revolutionary order, the petty bourgeois sees their individual livelihood, status, and slim hope of advancement threatened by collective transformation; this material anxiety drives them to support reactionary and often fascist forces that promise to defend private property and social “order” against the working class. Their reaction is not an ideological accident but class instinct: when the choice appears to be between losing their small capital or joining the stable exploiters, many choose reaction striving to join the exploiters.