Are you really sensitive to the minor/patch versions of node? I don't think it should make a difference whether you're using 20.9 or 20.12, and to me to that would be a bigger red flag.
Either way, I don't think many people are checking in tool-versions files. Most JS templates specify a range of node versions they work on and leave it to you to specify which one. I don't think this is unusual for most other languages I use, like ruby.