Sometimes, it takes a night's sleep and a fresh view to see the obvious. The problem was that the checkbox Live update at the bottom of the layer panel was deactivated (as can be seen on the screenshot of the question). I can't remember how that happened, I did not do that manually (at least not intentionally). Quite embarrassing to have overlooked someting as simple as this, but I hope this answer might help others with a similar problem.
Using a clean new user profile as proposed by @MrXsquared is great as a workaround in such situations, as you can continue working. Would be worth to create a copy of my current user profile to fall back to it in case of any other problem. The step-by-step proposal by @eurojam to re-create a user profile is another great possibility to consider in such situations.
Screenshot: checking the box Live update solved the problem:
