What does it mean to have a high p value but a very very low effect size? What can I conclude? Is it necessary to report the effect size when p=0.998?
There is a strong case for reporting effect sizes alongside p-values, as they both represent two different things. The p-value indicates certainty/uncertainty, whereas the effect size tells you about the magnitude of the effect. You can read this article for example: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/
And refer to this post:
You could report both the effect size and p-value, saying that the difference between the two levels of your variable is small and non significant for example.