Funnel plots were generated to assess for publication bias, but they were not reported as no outcome was reported by ≥10 studies. Where outcome measures were reported by ≥5 studies, the results were subjected to the Egger test.
You can theorically generate plots as soon as you have more than 1 study but the risk of underpowered method to detect any publication bias is very high. I think there is no magic number (maybe between 5 to 10 can be a rule of thumb). However, the robustness of your findings may depend on this number and of the importance of the true bias.
Several papers have addressed these topics:
Sterne JA, Gavaghan D, Egger M. Publication and related bias in meta-analysis: power of statistical tests and prevalence in the literature. J Clin Epidemiol. 2000 Nov;53(11):1119-29. doi: 10.1016/s0895-4356(00)00242-0. PMID: 11106885.
Deeks JJ, Macaskill P, Irwig L. The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. J Clin Epidemiol. 2005 Sep;58(9):882-93. doi: 10.1016/j.jclinepi.2005.01.016. PMID: 16085191.