Intuition on overall effects from climate change under different levels of warming
I think you're asking about the sort of outputs that are obtained from climate-change integrated assessment models [IAMs] And now you've got the right search term, your quest will get a lot easier.

You're doing the right thing: start with the IPCC reports. The next step is to follow through on reading their references. And then use google scholar or any proper academic search engine you have access to, to find more recent papers that have also cited those papers that the IPCC cited.

Here's a pdf on the PAGE09 IAM, an updated version of the PAGE2002 model used for the Stern Review. Chris Hope makes his PAGE model available to other researchers, on request.

Here's the UK's Committee on Climate Change report on IAMs

Here's the London School of Economics' page on IAMs.

And the TIAM IAM from UCL.

Google Scholar claims to have 3000 results from the last five years on IAMs and climate change.

As you can probably imagine, there are uncertainties piled on top of uncertainties in this field. The scholarly work on them nevertheless represents the best available set of expert expectations on the sort of damages we are likely to experience with different increases in the concentrations of greenhouse gases.