Rank von Neumann Test for autocorrelation with Ties using serialCorrelationTest()

If one has ties in their vector, how would the p-value from the Rank von Neumann Test be affected? I was reading the documentation for the function EnvStats::serialCorrelationTest() and it states that "When ties are present in the observations and midranks are used for the tie dobservations, the distribution of the Vrank statistic based on the assumption of no ties is not applicable. If the number of ties is small, however, they may not grossly affect the assumed p-value." I was wondering how would the increase percentage of ties in the data would affect the p-value? Later in the same documentation, it states that for small sample size for which the exact distribution of Vrank can be computed, the Vrank is rounded up with the no ties. So I would think that the higher the percentage of ties the greater change one would have to fail to reject null, yes? Now in the case of the beta approximation, would this still applies? And if yes, could one think that if the test find a "significant" p-value then chances are that there is serial correlation, however if the test is not significant, then in reality we could be missing the mark by a long shot depending on the percentage of the ties?

I guess my questions is fundamentally more a stats questions than a R question per se, but I am hoping that one of you could help me figure this out?

thank you Sab.