Go code contribution: license and patent implications?
No, it just means that if you contribute to Google's project, Google can still do whatever they want with it.
You are the copyright holder, of course. If your code gets included into Go, you become part of The Go Authors.
This is a common practice nowadays.
Effectively, through the Contributors Agreement you are sharing copyright with Google.
That means, in the end, Google has copyright over the entire codebase. This gives them the right to relicense the codebase however they want should they see fit. (Copyright owner determines license).
The primary goal of the CA is to ensure and assert that the contributor has the rights they are granting to the project (patents, copyright, etc.).
Some projects, for example, would want a patent grant, but are not interested in any copyright, as they have no intention of relicensing the project.
Mind, since the license is BSD, a copyright grant is really just a formality, because of how liberal the BSD license is in the first place.
To what extent does Google own any Go contributions?
You are not required to transfer copyright to Google. You still OWN the copyright.
You are not required to transfer ownership of patents to Google. You still OWN the patents.
In short Google does not OWN any IP that they didn't already own.
But you do grant Google the unlimited right to use and distribute your contributions, and you grant the right to use to downstream folks. Clause 2 covers copyrights, and clause 3 covers patent rights. Moreover you grant this as an irrevocable license (i.e. you cannot change your mind) and for free.
Do they have full rights to profit from these contributions?
There is no such a thing as "a right to profit" in a legal or moral sense. Hence "full rights to profit" is not a valid characterization of the rights that you currently have.
By granting Google non-exclusive, non-revocable copyright and patent licenses, your remaining rights are no longer exclusive. Google will be able to profit your contributions, but so will you. You will have reduced your scope for personal profit, but that was not ever a "right".