When and how did journal publications start to have such an important role in evaluating researchers? Wikipedia says that Newton published the laws in 1687 on Principia Mathematica. And in another page that:


  The first recorded editorial pre-publication peer-review occurred in 1665 by the founding editor of Philosophical Transactions of the Royal Society, Henry Oldenburg


However is unclear to me when and how publishing in highly reputable journals has become so important, in particular for judging a researcher's past research success. (For example, for evaluating researchers for purposes of awarding funding.)

I assume that it all started as a way to filter or deprioritize low quality research proposals or researcher, but that would make for other question maybe. When and how did journals start to have such an important role in science for evaluating researchers?
Widespread peer review in journals is a relatively recent phenomenon. Famously, Einstein and Rosen wrote an incorrect paper arguing that gravitational waves don't exist, which was rejected by a reviewer for Physical Review. The rejection made Einstein angry, and he wrote:

Dear Sir,
We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the—in any case erroneous—comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.
Respectfully,
P.S. Mr. Rosen, who has left for the Soviet Union, has authorized me to represent him in this matter.

This was in 1936, and Einstein had already published many papers by that point. It appears from his response that peer review was not yet common at that time.
(Source: &quot;Einstein versus the Physical Review&quot; in Physics Today.)
Googling this I stumbled across a blog post by Michael Nielsen who links to some historical papers on the growth of peer review that may interest you.