What is the best resource in your library for possible bavkground and historical settings for each psalm?
The Psalms Explorer within the L6 software will do. Also The Essential Bible Companion to the Psalms: Key Insights for Reading God's Word (not as indepth, but gives you good information such as Theme, Type, Author, Background, Structure, Special Notes and a Reflection for each Psalm). Hopefully these will help you. Here's the link for the Companion: https://www.logos.com/product/26723/the-essential-bible-companion-to-the-psalms
DAL
It depends for what kind of approach to psalms background you are looking for. In the academia, especially German scholarship, there can be a tendency to speculate on cultic occasions for individual psalms. This approach is rejected by many others as excessive in its presuppositions and methodology. At the other end of the spectrum, some lay resources can rely on the titles to the Psalms, but these are not believed to be original or necessarily accurate. If you are not looking for academic speculation, you may be better off reading a solid introduction to the Psalms that provide discussion of their historical background (in terms of the whole collection). It would probably include references to psalms believed to be post-exilic for instance. Pick up a solid commentary that corresponds to your readership/expertise level and check the intro.
The key words "possible background and historical settings" suggest that this is a form criticism question. And so I would turn to the volumes from Forms of Old Testament Literature commentary series to look to see what Dr. Gerstenberger says. After that I would compare it with the volume of the Old Testament Library by Weiser which I made a pb from internet archive and shared here. If I wanted more info, I would look at the bibliographies of the FOTL volumes and also the WBC volumes on the Psalms.
Of course, this can turn into a rather deep hole, but there are a lot worse ways to spend an afternoon.
Thanks so much for the suggestions. I appreciate the leads.
I'll be looking into that resource. Thanks!