Is the version released yesterday
LimeSurvey version 4.0.1
LimeSurvey build 200120
considered a stable release?

I guess this very much depends on your definition of "stable".
www.limesurvey.org/about-limesurvey/download
Base on this page I guess the core developer team considers it a stable release.
Personally, I would probably wait a couple of weeks/month before using LS 4 in a productive environment. However, I was "out" for a couple of weeks and have not tested LS 4 yet, so this is purely based on past experiences.
If LS 4 is stable enough for your purposes only you can determine. So I recommend to download it and test it thoroughly and see what how it feels.

I have been testing for serveral months and have reported certain problems that have been fixed. Each release has been better, but still marked as a beta. The release yesterday is the first one marked as "stable".
As with all new software there is both a learning curve and a need to test to be sure it fits your needs.
My question is for the developers who now must feel this is solid enough for production. Version 3 is frequently updated for minor issues and I would expect the same for 4.
But version 4 offers a few significant features we need. So now is the time to move "some" of our production there and continue to watch it closely.

To all those who have worked on the product (and those who have tested and reported) a big THANK YOU.

Hello @GuernseyResearch!

Thank you for your message and wishes! The community deserves all our appreciation

The simple answer is: we, LimeSurvey GmbH, consider LimeSurvey 4 to be stable.

However, as @holch underlined above, we may have not yet uncovered all the bugs/pushed all the required fixes. But, we will try to fix the reported issues asap and release at least once a week. The new features need also to be ironed out - we are looking forward to seeing your recommendation & advice (encryption, file manager, user permissions, etc.)!

I am not sure how you are using LimeSurvey 3 for production at the moment. Perhaps you can run a parallel LimeSurvey 4 instance and check if it works as expected (plugins, themes, question themes, etc.). If not, create full reports and try to add themes/.lss files whenever possible to make the developers' life easier.

If something is unclear or you want quicker replies, look for help in the IRC channel - I am most of the time online there.

Several months ago we ported over the LS3 work to LS4 so we could test and provide feedback. I maintained the updates on both LS4 and LS4 over time.
We have made some changes in our production work so I plan to port all that over again now that you believe LS4 to be stable. This will allow is to run "production" on LS4 watching carefully for any issues.
Thank you for the ongoing work and for fixing those items I reported.

Installed LS 4 in our test branch and it's working just fine, comfort update included so well done all.

Is there any place I can find an overview of the new features? Can see the new survey groups and central participants database, otherwise the updates on Github are useful but a bit too granular. Sorry if I'm missing something obvious.

Thank you for your feedback!

Unfortunately, there is no place where all the features are described (at least not at the moment). We are still improving the new features that have been just introduced - a document will probably be available in a couple of weeks when the new features will be ironed out.

Till then, please test LS 4 and report all the issues/feature requests on bugs.limesurvey.org :)

Thanks for the response! Even a list of eight bullet points would probably be worth sharing if you had them.