The Shapiro-Stiglitz model. Why under full employment do unemployed workers find jobs instantly? Under the Shapiro-Stiglitz model the No-Shirking Condition is:
$$w=\bar{e}+\left( \rho +\frac{\bar{L}}{\bar{L}-NL}b \right)\frac{\bar{e}}{q}$$
Where:
$\bar{e}=$ exerted effort by employees
$\rho=$ discount rate
$\bar{L}=$ total number of workers
$N\bar{L}=$ number of employed workers
$b=$ job separation rate
$q=$ shirking detection rate
(From Romer's Advanced Macroeconomics 3rd edition, pg. 453)

[The no-shirking condition shows] the wage that firms must pay to induce workers to exert effort. When more workers are employed there are fewer unemployed workers and and more workers leaving their jobs; it is easier for unemployed workers to find employment. [...] At full employment, unemployed workers find work instantly, and so there is no cost to being fired and thus no wage can deter shirking

My Question
The definition of full employment is:
(Source from Investopeida)

Full employment is an economic situation in which all available labor resources are being used in the most efficient way possible. Full employment embodies the highest amount of skilled and unskilled labor that can be employed within an economy at any given time. Any remaining unemployment is considered to be frictional, structural or voluntary

Based on this definition is appears that even under full employment workers do not find work instantly under the Shapiro Stiglitz model. What exactly am I missing?
I think that the confusion is caused by the different meaning of "full employment" in both contexts.

In the Shapiro-Stiglitz model, full employment in the sense that $\bar{L}\rightarrow LN$ implies that the job finding rate $a\rightarrow \infty$, which means no frictional unemployment.

In the other definition, full employment is merely defined by any remaining unemployment being only frictional (or structural/voluntary, not important here). Situations of no full employment could exist, for example, due to minimum wages, according to this definition. This view considers the unemployment arising from workers being laid off and waiting some time to find a new job (frictional unemployment) as a technological necessity that cannot be avoided so as to further increase efficiency.

Last but not least, please note that your quote from Romer concerns the labor supply curve only, while the employment rate will be determined in equilibrium.