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Does the omitted variable bias still exist if the omitted variable is not related to any...

Does the omitted variable bias still exist if the omitted variable is not related to any explanatory variable but is impacting the outcome variable

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yes, because In statistics, omitted-variable bias (OVB) occurs when a statistical model incorrectly leaves out one or more relevant variables. The bias results in the model attributing the effect of the missing variables to the estimated effects of the included variables.

OVB is the bias that appears in the estimates of parameters in a regression analysis when the assumed specification is incorrect in that it omits an independent variable that is correlated with both the dependent variable and one or more of the included independent variables.

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