It is much more common for me (and again, most people) to google search
I will have to take “most people” as speculation. We were actually missing site search for a few years after Google shuttered GSS, and an issue to bring the site search feature back was one of the most discussed and voted issues we ever had. My own experience is that many people do want to use site-search and I’d like to find ways to encourage it even more because it is effective and efficient.
Other packages usually have the most recent version as their first google hit
This is controlled by Google, I am afraid. I am not sure what we can do. We publish canonicial URLs pointing to “latest” on every page, which AFAIK should direct google results to “latest”, but does not seem to have desired effect. If there is anyone who is an expert at optimizing GSE results who would like to work on this, I would love help, because I have tried everything I know to try, and am frankly past a point of frustration with it.
Packages that don’t have this usually have a link at the top of the old docs that warn that the documentation page you’re looking at is out-of-date,
I am confused about this point. We have long had such a banner at the top on old versions (and also on pre-release versions). Are you saying you are not seeing the bright banner like in the screnshot below on your system/browser?
Edit: older versions are even more stern:
