Let's break this down.
Your title indicates that you want a copyleft license - this rules out all permissive licenses.
Just for the record: "copyleft" means that any downstream recipients who distributes adaptations of your framework, is required to offer anyone who receives an adapted work, source code for the adaptation, under the same license (or one with identical terms).
My goal is for people to be able to use the framework to develop their own projects and only be required to release any changes made to the framework back to the community i.e. they should not be required to publish their project's 'content' as open source.
That requirement will not be a problem, the separation between "code" and "content" (sometimes called "assets" or data") is well-known, and no copyleft license requires source code of "content" that is simply read by the program to be regarded as part of the adaptation.
The GNU LGPL looks like it might be a good fit but seems to have been written with a heavy focus on .dlls and code.
As noted in the answer by Calinou, since 2.1 it has broadened.
I am also concerned that anti-DRM clauses may limit adoption.
All versions of Creative Commons are anti-DRM.
You may not distribute, publicly display, publicly perform, or publicly digitally perform the Work with any technological measures that control access or use of the Work in a manner inconsistent with the terms of this License Agreement. (CC BY-SA 1.0 & 2.0)
You may not impose any effective technological measures on the Work that restrict the ability of a recipient of the Work from You to exercise the rights granted to that recipient under the terms of the License. (CC BY-SA 3.0)
The Licensor waives and/or agrees not to assert any right or authority to forbid You from making technical modifications necessary to exercise the Licensed Rights, including technical modifications necessary to circumvent Effective Technological Measures. (CC BY-4.0)
The language has been softened in ver. 4.0, from banning it outright in version 1-3, to allowing circumvention of DRM, in ver. 4.0.
As for the software licenses, there is no anti-DRM in GPLv2 or the LGPL.
GPLv3 and AGPLv3 is clearly anti-DRM, with a provision to circumvent, similar to CC BY-SA 4-0, so if this is a concern you should avoid those.
Some of this framework will be non-code files (sprites, textures, sounds, etc) that I would like to be covered by the same license.
Normally, I would not recommend using a software license for non-code. However, in this case, all the CC licenses are off the chart because they're anti-DRM. The GFDL is copyleft and allows DRM, but it is (IMHO) painful to use because its over-the-top formal requirements. Other content licenses I am aware of (i.e. Open Publication License, Free Art License, Academic Free License) are either non-copyleft, or they are anti-DRM.
This rules out using any of these for your project's content
This means that we're left with free software licenses for the content as well.
The choice from there is how "strict" you want your copyleft to be and how much license compatibility you want to offer.
LGPLv2.1 and LGPLv3 are "weak" copyleft licenses that allows downstream recipients to combine your framework with anything, including games that are sold commercially, without giving anything back to the community. The requirement to share adaptions does not trigger until they alter your code and distribute the resulting program. If this is OK, then you should use one of these for the framework (I prefer LGPLv2.1 because I think it is clearer that GPLv3 - but this is a personal preference).
GPLv2 is "normal" copyleft that requires both adapted and linked source code to be shared (if some derived work is distributed). This does not disallow use in commercial games, but the source code of any game that is distributed commercially must be given back to the community. If you want this stronger type of copyleft, then GPLv2 seems to be the right license.
To avoid any copyleft confusion, you should specify (e.g. in
README) that the while the non-code assets are under the same license as the code, they are included as "mere aggregates" and do not trigger any copyleft clause on user created content.