It's now a WebExtension, which means it will work in Firefox 57+ (and possibly eventually Chrome, if they end up supporting the same APIs), and uses the new Sidebar APIs that the new Notes experiment also makes use of.
If that doesn't fit your use cases, there are also quite a few new tab sidebar WebExtensions popping up that aim to replicate existing more sophisticated tab management extensions like Tree Styles Tabs (https://addons.mozilla.org/en-US/firefox/addon/tree-tabs/), and others that try to innovate on their own terms, such as Sea Containers (https://addons.mozilla.org/en-GB/firefox/addon/sea-container...), which makes use of the new Containers experiment.
Overall there is a huge amount of very promising new development in the WebExtensions space, and this is exactly the kind of innovation I had hoped WebExtensions would encourage.
Looks like this: http://i.imgur.com/nhGpHYt.png
Each section can be hidden individually, so if you just want the search box or just the websites you frequently visit or don't want stupid articles recommended on your newtab-page, those are all things you can do.
Seems like they took out the recent activity thing, but no idea if this is finalized already.
[1]: https://testpilot.firefox.com/experiments/activity-stream
I loved the experimental home page and the Tab Center [1]. I really hope it continues to live.
[1] https://github.com/bwinton/TabCenter