Interpreting funnel plot asymmetry can be quite tricky since it is primarily a subjective process. Egger test is arguably more objective since it has a precise mathematical component. Nevertheless, the Cochrane Handbook suggests that funnel plot assessment, either by asymmetry determination or Egger test, is unlikely to be conclusive when the number of included studies is less than ten (https://handbook-5-1.cochrane.org/chapter_10/10_4_3_1_recommendations_on_testing_for_funnel_plot_asymmetry.htm).
This reference might be useful to you: https://training.cochrane.org/resource/identifying-publication-bias-meta-analyses-continuous-outcomes.
Funnel plot assessment is the gold standard assessment for publication bias. You do have to look at a hundred or so before you get good at it though. However, the Duval and Tweedie's trim and fill adjustment is more important. The trim and fill adjusts the overall effect size for the presence of funnel plot asymmetry. You can have marked funnel plot asymmetry but the adjustment to the overall effect size could be minimal.
Both can be very useful. I just worked on a meta-analysis in which I used them both. Funnel plot seemed asymmetric, however, I would not say that this was publication bias, since the funnel plot suggested a lack of studies with high estimates (there were 12 studies), and that definitely would not be due to underpublication, so my thesis was that it was not publication bias and Egger`s test with its non-significant p supported my thesis. So why not combine those tests?