TLDR: over time, Apple transitions from one technology/development platform to another. author calls this an "invisible" strategy because... it's done properly and methodically.
I can’t think of a single transition that Apple botched. They even had a good transition strategy from the Apple //e to Mac for users with the //e card.
Apple II->III? Mac->Copland? Mac->Taligent? Apple IIgs->Mac? HyperCard->(nothing)? Carbon 32b->64b (as originally promised)? FCP 7->X? iMovie HD->08? iWork '09->2013? Mac Pro 2012->2013->2019?
It depends on your definition of "botched", but I can think of lots of examples of cases where Apple either gave up, or essentially reverted their changes, in the face of public outcry or technical hurdles.
I wouldn't really call the IIe card a "transition strategy", either, any more than Mac86 was. It was a kluge to add another entire computer as an add-on card. It didn't help move your programs or data at all. It also only emulated a IIe (8 years old at that point), not a IIgs (only 5 years old). It was only a 'transition' for the absolute penny-pinching-est buyers, i.e., education.
Some of your examples are pertinent, but I think calling MacOS->Copland, MacOS->Taligent, HyperCard->(nothing) "botched transitions" is a bit disingenuous.
Copland never shipped, and as such was not a transition at all, because the public was not directly involved in the internal failure. Taligent basically never shipped anything, and so the same argument applies.
The replacement OS that Apple actually shipped (OS X) aided a legacy transition that I think went down basically as well as it possibly could have (given the inherent dissimilarities between the two OSes).
HyperCard was merely killed off, so there was clearly no transition at all. That's like saying Newton->(nothing) failed as a transition.
The Apple III was backwards compatible with the Apple //.
Copland and Taligent never shipped to developers or users so neither wasted time on it.
I had an Apple //e card. Using the included software, you could setup a ProDOS partition on your hard drive, and copy files from the //e to the Mac. Apple bundled converters that you could use to convert AppleWorks documents to Mac app documents.
Mac86 sucked but the DOS Compatibility Card for the PowerMac 6100/60 with a 486DX/2, a dedicated sound card, and the capability of adding 32MB of dedicated RAM was quite good until Windows 95 came out and it could only use 16 bit drivers. That was my second Mac.
I am quite curious about the HyperCard thing. I've come to the Apple ecosystem quite late so I have never experienced this but it looks like some of the current design tools such as InVision and also Powerpoint/Keynote. Am I mistaken? What made HyperCard so great? If it was so powerful why isn't there an extremely popular alternative? It does not look like something only Apple could ship.
Ok well if your metric for "botched" is that developers had a hard time, the general 32-bit Carbon to 64-bit AppKit transition would have to count. :) App Sandbox perhaps too...