I've got an R7 but I mainly use it to anchor my bird/wildlife kit. But I recently got an R10 for a small, urban-prowl kit.
I started out with that SIgma 18-50, and I like it well enough. Fast, sharp, tiny, but not much zoom range, as you're finding out. My wife and daughter have kind of appropriated that rig. My big DSLRs intimidate them, but the R10, they're into it. The R10 doesn't have IBIS, the Sigma lens doesn't have IS, and my girls, as much as I nag them about it, haven't really learned how to hold a camera. Along with the short zoom range, I decided the Sigma wasn't the lens for them.
So I got an RF-S 18-150. It's not much bigger than the Sigma, considerably slower, but plenty sharp. And it just feels easier to use, plus it's got IS. We do most of our shooting outside so slow is mostly OK. If I need it for indoors, I've still got that Sigma 2.8. I also picked up a 100-400, which pairs with the 18-150 nicely.
You mentioned concern over the 55-250 paired with the R7 sensor. I'd never thought about that. The R7 does have a jam-packed sensor. I mostly use mine with L lenses. When I did use an R7 around town I'd usually pair it with an EF-S 15-85 that I carried over from my xxD days. It's a good, sharp lens, with an ideal zoom range on an APS-C body. I wish they'd make an RF version. It's short and stubby on a DSLR, but it's long and front heavy with an RF adapter. If you're interested, I might sell you mine.
If you want to continue with what you have, and maybe add a 100-400, you can put that R7 sensor to use. It handles crops very nicely. Just shoot loose at 50mm and it will crop down to an 80mm or 100mm angle of view no problem.
I've never put my 18-150 on my R7. Now that you brought it up, I wonder how that would work on an R7 sensor. Did anyone ever mention that lens when you were looking at the 55-250?
Sadly, there are not a lot of options for APS-C lenses at the moment and I don't see that changing soon. Canon seems to have put that on the back burner.