The jobs do exist, but I've no idea how common they are
I am in the US, but I work for an international company for which the UK members have a strong leadership presence. My boss' boss is in the UK.
I'm a generalist. I know something about a lot of different things, can use that to solve lots of problems, or create lots of solutions. And I've got a job where that's basically what I do professionally, where the breadth of my skills is basically specifically why I'm valued, and I'm paid very well. I've been where I'm at for some time, though, so I can't speak to how easy it is to find a job like mine, and it's something I do worry about should this job disappear or become unsavory. I *can* tell you my team wishes we could find more people with a breadth of skills.
Where I fit in best is in a place where specialists exist in their own silos. You have developers, DBAs, sysadmins, storage teams, and networking gurus. In places that divide specialties up like that, you often benefit from someone who is a bit like a business analyst, except instead of being the interface between developers and customers, they face the other direction, interfacing between developers and infrastructure / middleware.
What we find is that the developers often are wildly ignorant of the implications of the system's (virtual) physical design. The infrastructure teams often have no time to learn the ins and outs of the applications, in order to tune their systems for them. I help the developers create systems that won't be rubbish on the basis of the systems on which they run, and help the infrastructure folks design hardware that won't be rubbish for the needs of the application.
The challenge is in finding an organization that values this role. Not everyone does, and that's clear even within my company. What seems to make the tuning and problem solving skills valuable to people is when they're strapped for budget and they need to expand their system or make their existing scale of system run better. Tuning things can increase concurrent users on existing footprint or reduce infrastructure for same performance. And even in a cloudy context, the ability to achieve those things can be valued. But I fear that may be rare.
I would never do project management. It has nothing to do with why I'm in IT, and requires primarily the exercise of people skills, not technical ones. If I lost this position, I would look for a job as a systems architect - someone who looks at the big picture of software, infrastructure, APIs and whatnot and assembles it into a solution. I see a PM as someone who drives all the people involved to implement that vision. I would want to be the person creating the vision itself.