MS's problem is that, at least from what I'm seeing online, a narrative is starting to form that may be hard or virtually impossible to shake off if they don't nip it in the bud sooner rather than later. In that way I actually do think seeing these early days in a PS1/Saturn light is very apt because there's a lot of parallels, but MS has means of resources (and better corporate synergy) to improve in ways SEGA lacked in the day.
Can MS honestly afford to wait until Halo Infinite (provided it has much improved visuals) or Starfield are ready in order to show off what the Series X can do? IMHO, no. By then it'll be too late to change what narrative settles in by then, because by that time Sony will have R&C Rift Apart, Horizon Forbidden West, GT7 and perhaps even Ragnarok showing their chops in the 1P suite and visual prowess department in addition to what Demon's Souls Remastered and Miles Morales are already doing.
So MS can't rely on Halo Infinite and Starfield for that. They need to make sure they're giving as much technical assistance to the Bright Memory Infinite, Exo-Mecha and Scorn teams as possible. Those games are scheduled for early 2021 IIRC and MS needs to start swinging that momentum in terms of visual narrative back to their favor after this launch period starts to wear off. Those games (and whatever other Xbox ecosystem exclusives are due in early/mid 2021) need to do their best to shut down any growing speculation on their platform having technical bottlenecks, whether it's CPU-related, GPU-related or SSD I/O related. Waiting and waiting isn't going to do much for too much longer.
I'm confident they can do it but it'll be some work to pull off, that is for sure. At least Gamecore seems to have stabilized and is getting out to more 3P devs now, which is a solid first step.