PS3 is 100% a big failure. I mean:

1 - It manages to have so much loss that the profits with PS and Ps2 practically melted.

2 - It loses absolute market dominance of the Ps2 and allows rivals to gain market share.

3 - Lose several traditionally exclusive games, such as GTA and Final Fantasy.

4 - PS3 almost made Sony leave the Console market, and the success of the Ps4 saved the brand:
https://www.playstationlifestyle.net/2020/08/01/how-ps4-success-saved-playstation/

I could continue, but I believe this already shows the size of the failure that was PS3. Luckily it planted the "seed of humility" that brought Ps4 to life.

I feel like Xbox One was a victim of Microsoft not having a plan on how to balance their support for both PC gaming and console gaming. Only recently they seem to know what they are doing.

Microsoft stopped reporting hardware sales of the Xbox One it was doing so poorly. It was a categorical failure. The 360 improved sales in every region, including Japan, over it's predecessor. And that was with RROD stifling it's sales potential. XB1 It did so poorly in Japan that publishers wouldn't even bother localizing games released elsewhere for the region.

Nope since it lost a lot of market share and did horribly compared to Microsoft's expectations. Phil Spenser said in a 2016 interview that the team had a goal of hitting 200 million and only doing a quarter of that had to have been a big reality check.

The XBOne was succesfull in the goal of undoing the damage that Don Mattrick did to it at the beginning of the 8th gen, if it hadn't done that it would have ended up with even worse numbers. But it wasn't good enough to compete with the PS4 first and the Switch afterwards. Thus all of Microsoft's effords in reinforcing the XBox brand with the studio adquisitions.

^ this.

XB had a PR nightmare start to the gen, but a year and half or so, with better games output than PS4.
After that, the PS4 just had better games releases rest of gen.
XB1 didnt end on a high note, it was the "wait for next e3! console", and the "60 meta games" one.

I dont think it redeemed itself.
Xbox fans, basically where okay to just jump to a new gen, and hopeing things would be fixed by then.
MS did give them some hope, in going out and buying alot of new studios (which means things likely will be as well).

Was it successfull in terms of profit? maybe.
Was it successfull in terms of endeering it to xbox fans? or growing the fan base? I seriously doubt it.
I think alot of less hardcore xbox users, after the XB1 gen, decided to go PS5 instead of next Xbox.
Simply because of getting burnt on the xb1.

I would argue that the PSP saved the Playstation brand in those days. Without the sales and profits of their handheld, their videogame bussiness would have really looked grim.

But Playstation users loved it.
It cost sony (in terms of hardware and software), but they spent to fix it, though software output.

Economically it was a huge failure.
But it won hearts, and PS fans went on to lateron get new PS's.

Sony values its consumers, to spend, even when they probably shouldn't have.
MS basically gave up on the XB1, and just let it coast the last few years, into next gen.
Nintendo abandoned the Wii U as well, as soon as they realised it wasnt doing so well.

I'm not sure if that argument holds water when they abandoned the Vita after its lackluster beginnings. Especially considering that the PSP was the machine bringing them money during the 7th gen, while the PS3 was bleeding them white.

I understand your point, PS3 was a console that had enviable support, especially in the second half of its life, and I personally consider it to be better than X1 and WiiU in the area of "delighting users" and "delivering great games" but... .

It's impossible not to take into account Sony's market loss and financial losses, and other factors I mentioned... Ps3 was a failure, I respect your opinion and those who disagree with me, but there are many disastrous factors related to the console .