ö > oe is standard German spelling reform. Similarly with umlaut over a and u > ae and ue. According to a law of about 15 years ago, German publications – newspapers, magazines, examination pupils – are supposed to use the reformed spelling, but I don't think that applies in Switzerland or Austria. In any case, mixing the two spellings in one article is sitting on the fence in the worst way.
I presume the fern effect is something to do with uncoiling...
I don't think that was a reform. The 2006 change was a partial retraction of the 1996 reform, but that had been mainly about ss, sss, and friends. Other spellings were tidied up to make them more regular, but only a few with umlauts coming or going.
But the ae, oe, ue spellings were earlier that the umlaut, which came in only with printing. This inserted e (or occasionally other letters) was a common trick in Latin when it was applied to barbaric tongues with weird new sounds. Old English also had the "frontalised" vowels ae (written as a ligature and regarded as a letter in its own right) and ue (for which y was invented, but it soon shifted its sound in English but not in Danish). There had been runes for both and for ue, which fell out of use just as the Latin script took over.
I suspect any change in news media usage was related to compatibility issues with non-German PCs and other devices, and especially their keyboards. In which case the timing is a bit ironic, coinciding with the general adoption of Unicode.
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