Pfthb

In my Literature Review, I mention the authors of the published papers I use and the results found in their study. My question is whether I should reference the author's credentials alongside the field in which they belong to or is this unnecessary?

Ex.1 (With)
"Joakim Ruist, a researcher in the department of economics at Gothenburg University, studied the effects of refugees on public finance, finding similar results."

Ex.1 (Without)
"Joakim Ruist studied the effects of refugees on public finances, finding similar results."

Ex. 2 (With)
"In contrast to the conclusions drawn by Ruist, Alden and Hammarstedt, and Storesletten, Bo Rothstein, Professor in Political Science at University of Gothenburg, argues the sustainability of the Swedish welfare state is not under threat by refuge migration."

Ex. 2 (Without)
"In contrast to the conclusions drawn by Ruist, Alden and Hammarstedt, and Storesletten, Bo Rothstein argues the sustainability of the Swedish welfare state is not under threat by refuge migration."

What matters is the work presented in the paper. So you just write

Ruist [1] studied the effects of refugees on public finance, finding similar results.

There are occasions when inclusion of author credentials is useful (especially in the general press), academic publications (generally) aren't such an occasion and I've never seen such an inclusion in academic publications. That said, I wouldn't be surprised if there is a discipline that includes author credentials in publications.

TL;DR: Without

I have the impression the academic discipline may factor into this. I cannot recall ever reading a phrasing like your "with" examples in any STEM publication, but in the social sciences this may easily be different. From my limited experience with social sciences, many papers seem to have a bit more of a "conversational" tone to them, and your "with" examples would probably fit in more in such a style than with the fairly dry and reduced style of writing that is often preferred in STEM.

That said, what I have sometimes seen as a mixture, as in:

Conversely, researchers at the University of Gothenburg [1] have stated ...

That is, I have seen people mention the place where the research was conducted, but not the credentials. Obviously this would happen if it could have at least some tangential relevance where this research has been conducted. In your example, if the other researchers were outside of Sweden a reader may be inclined to put more trust into a statement on the Swedish welfare state from researchers actually working in Sweden versus people who only look at it from the outside. It goes without saying that this is simply not the case in most STEM publications (although, as I wrote, I have seen it come up very occasionally).

I also have never seen in a literature review mentions of an author's credentials unless it is directly relevant to discussion. For example, during certain periods of time two different universities might have had different approaches to a philosophical orientation. In that case, noting where an individual was located at a given time might give some insight. So, an individual at the University of Chicago for Economics (neoclassical approach) might be contrasted with someone from the Austrian approach. So:

John Smith [1], while lecturing at the University of Chicago, astounded his colleagues by suggesting massive federal expenditures.

Without some note about the UofC, the astonishment would not make much sense.

The American Psychological Association (APA) guidelines suggest that academic credentials are omitted. There is a blog post here where the guidance is that:

Typically APA Style reference list entries and in-text citations do not include the authors’ academic credentials or professional titles.

This assertion is somewhat associated with section 2.02 (APA 6th edition). The MLA has similar guidlines.

There is a note that if the credentials "are relevant to the discussion" they may be included, which I think follows with my opening observation. This blog post on the MLA also suggests the omission of qualifications unless it directly makes a point:

You might, however, explain the qualifications of an author in the body of your essay if they are helpful in making your point or refuting a claim

So, based upon the OP's examples, the answer would be "without" as the titles and affiliation are not directly relevant to the discussion. The APA and MLA guidelines are in agreement on this point, I think.