Try doing this on a 5 year old project. You'll very likely end up in dependency hell.
There is a solution though - use of nvm and .nvmrc (to control the version of node and npm that you use), and use of npm ci (which installs packages as they were at the time, rather than installing newer versions than specified in package-lock.json (because too many devs rarely ever pin versions) instead of npm install / npm i).
I rarely if ever get version mismatches for a normal npm install because upgrades by default only do minors. If a package has a breaking change in a minor it's not a JS issue, it's not a npm issue, it's a "this package author made a breaking change in a minor" issue.
And regarding nvm: That's obvious. This is the same for almost any runtime. If you have the wrong jdk version it doesn't work, if you have the wrong (whatever iOS uses for xcode) version it doesn't work, if you have the wrong version of gcc it doesn't work.
Obviously wrong is not always the same, more up-to-date versions of gcc can compile older programs (maybe) but that's also the same for Node unless otherwise specified in the packages.
Lol what a great way to describe what running a simple "npm install" entails.