Levene test for equal variance

I would like to run one-way ANOVA test on my data. I saw that one of several assumptions for one-way ANOVA is that there needs to be homogeneity of variances. I have run the test for different data-sets. I find sometimes my p-values are larger than 0.05 and for some datasets it is smaller.

As I understand, if the p-value is smaller than 0.05, then I can reject the null hypothesis and tell that the variances are not equal (and then it makes sense to use ANOVA?)

The problem is that I see in different sources diferent conclusions: in some they run ANOVA if they reject the null hypothesis, for some they run ANOVA if they cannot reject the null hypotheis. For example,

here it says that if is smaller we can run the ANOVA:

But here it recommended that p-value0.05

To me, intuitively, it sounds like p-value should be greater than 0.05 but I would like to get clear answer regarding that.