I am in the process of building a new site which I will be designing the theme for.
I had previously designed with Toolset Starter Child but when that was discontinued my next site build was based on _s with Layouts integration where the entire site was designed via Layouts (code example below).
If this is the case I need to avoid Layouts for my next theme build, so my question is: is there another way of achieving what was previously possible through Layouts integration with Toolset or is my only option to be writing the php myself?
I don't have a lot more news other than what you can see on the Layouts-Theme integration page.
Layouts isn't being retired, there are too many existing sites that use it, but given that a page builder is now included in WordPress core we determined that our efforts are best directed towards making that experience as good can be, rather than investing resources on adding features to Layouts.
For some time now Layouts has been intended to work with any theme and just replace the main content area, rather than the initial vision and implementation of integrating it with themes to be able to design the entire page.
The Gutenberg editor isn't able to do that yet, but it's the direction we are heading: hidden link
If you are making a theme and want to use Layouts, we'll continue to maintain it (fixing bugs and compatibility issues) but won't be adding features.
You might be interested in the custom theme my colleague Beda made to work with Layouts, which is well documented and can be used as a starting point for your own projects: https://github.com/TukuToi/MinimaX1/
Just be aware that it is not a Toolset product and if you need support you would need to file issue in its github repo.