For publications and published thesis, BioRender requires a paid subscription, for presentations it is free though. For cell biology and biomedicine, there is a free clip-art collection from a pharma company ("Servier") that can be used with PP or graphics software. For pathways, you can still use KEGG maps after obtaining permission (https://www.kegg.jp/feedback/copyright.html). Most other needs are covered by r-packages and especially ggplot + (good) vector graphics software (Illustrator or Inkscape), eg.:

• R-package to produce anatograms: https://r-charts.com/miscellaneous/gganatogram/
• vector drawings of different cells and celltypes: https://www.swissbiopics.org/ (usage is free, CC-BY SA)
• drawCell: https://github.com/svalvaro/drawCell a new R-package for visualizing cells and highlighting compartments using swissbiopics API
• for any other domain (protein structure, -Omics, sc-Omics, genetics, phylogeny, networks, metabolic modeling, ...) there are sheer endless possibilities:
  • see the BioTools registry for a curated overview (>1600 tools)
  • Bioconductor View: Visualization (>500 packages)

Some more recommendation:

• Use vector formats (SVG, PDF) whenever possible
• FigTree (to SVG) for phylogenetic trees
• I use Jalview for multiple sequence alignments (yes, it`s possible to get ok graphics out of it)
• Chimera makes the prettiest protein visualizations
• Circos plots circles
• when making figures, keep them in SVG as long as possible and use proper version control (e.g. git)
• print your figure on A4 paper, all text must be readable

In my opinion, there is no such thing as "publication ready visualization tools", best one gets is "near publication ready". That is because a good figure is readable, didactically adequate, and conveys the story of your paper. From my experience one always needs to edit figures to at least:

• change fonts and sizes (e.g. in phylograms, the species labels must be italics)
• rectify overlapping text (beware of the typesetting team)
• highlight regions of interest and add additional annotation
• combine single figures into panels

Don't bother about specific tools for tables, use word-processor's built ins, LaTeX tables (e.g. booktabs), or Excel. Now you should have all the options you will ever need.