As far as T-cell immunity from actually having gotten the disease, there's quite a lot, actually.

Here's a search for all the articles (the only magic bit being that that kind of immunity is called "convalescent"). I'd say pick some recent ones from a trustworthy site (e.g. PubMed), but, as you can see, there's plenty.

There's also evidence that this immunity carries from recovering from a previous strain to immunity against Omicron - and I recall seeing at least one report that the same thing was happening between alpha and delta (but can't find it - this was back when delta first appeared so very out of date).

OK, this does NOT say we're safe from ANY future strain. It's just starting to look a bit like that - and I'd argue that convalescent T-cell immunity would probably be better than that from vaccination as the T-cells would be sensitized to a lot of different parts of the virus when there was an actual infection. mRNA vaccination produces T-cell immunity to the spike only.

As far as "those without recent infection", I've been trying to find any indication that people with previous infection are getting hospitalized or dying at a greater rate than the vaccinated and I've been unable. If you find one, could you please respond with a link? I'd love to look at it (and maybe change my thinking, sad as that would make me).

Thanks!

[edit] I think I've found some. Have to wrap my head around the Cox proportional hazards model to understand WTH they are saying [/edit]

Oh, and Omicron is actually less fatal than Delta for the unvaccinated. It's just that there are enough more infections to swamp that lower fatality rate.