Considering the moves within Microsoft to focus more on a multiplat approach probably came before the release of the Series X, definitely no chance.

Sure feels like it at this point, but I dont think in the early stages it was. We just expected much more support.

It was unwinnable based on how much Microsoft damaged itself with the Xbox One launch proposals and the decisions that were later on being made by Phil Spencer, such as the refusal to make exclusives for Xbox as well as their general mismanagement of first party studios and IPs. They had good chances to do better than they did with the Xbox One, but that was undone by additional bad decisions by Phil Spencer, most prominently the recent move to turn Microsoft in a complete multiplatform publisher.

The only possibility to beat the PS5 required Sony to commit PS3-like blunders to create an opening, but Sony didn't. Unwinnable, however, does not imply doomed to self-destruction of one's console business. Based on the circumstances, the Xbox Series would have been a generation to rebuild consumer trust and work as a setup to become a serious challenger again during the generation afterwards.

Nope, no chance.
SNY was highly unlikely to screw up PS5 after living through PS3 and witnessing XB1, so MS could only hope to claw back market share with XB Series.
XB Series has fallen even further because for any error SNY made with PS5, MS made an error as bad, if not some worse.
MS as a company has never been great at selling large volumes of hardware to the average joe consumer.
Micro-Soft.

Agreed. Xbox was a failure that generation by comparison.

Microsoft is doing a full pivot and embracing the PC community, which is far larger market.

No point selling lots of hardware and not making money, that's not successful.

I’ve see people say this quite a bit but there is a difference between Nintendo being profitable and GameCube being profitable.

Would Nintendo have posted profits in 2001-2006 without GBA/DS?

Yeah I feel like Starfield was the system's last chance to prove its viability; after that game combined with steep holiday discounts failed to move the needle, it was essentially over and MS threw in the towel.

21 million sold is pretty much a failure I'd say, especially when your competition sells 160 million and your previous system sold 32 million.

Making a profit is not a failure. Gamecube wasn't a rousing sales success, but it also wasn't a failure. It's never a failure if you profit. 

As zorg points out, we don't know if Gamecube in itself was profitable cos their income in those years largely came from their handhelds.

Xbox's only chance was a repeat of Gen 7. They would bring the games and economically priced hardware people would want while Sony screwed up the launch and launch window. It's true PS3 won out in the end by number of consoles sold worldwide but not by a lot. And Xbox 360 lost less money for Microsoft than PS3 did for Sony.
The gen was pretty much unwinnable without Sony screwing up, but a lot of us (me included) thought Xbox Series X/S could soar past 50 million units and very likely outsell Xbox One. We underestimated the simple lack of enthusiasm for Xbox hardware that Microsoft had fostered with Xbox One. Why buy an Xbox Series when you can stick to your Xbox One or get a PS5 or PC?