Canon EF-S 10-18mm f/4.5-5.6 IS STM is a low cost ($300) and compact solution. It's also one of the few ultra-wide zooms that has image stabilization and it offers excellent image quality. It's a bit plasticky, but that helps keep it lighter weight.
Canon EF-S 10-22mm f/3.5-4.5 USM is a more expensive (on sale heavily discounted to $429 right now), but better built, slightly larger and heavier, but also up to a stop faster lens. An older lens, it's not an "L-series", but clearly better built than the above lens. It also has excellent image quality. This lens has been around for a number of years and should be easy to find used for some savings, if you wish. Also check if it's offered refurbished from the Canon website. (I might consider the more lightly built 10-18mm refurbished, too... but would be a little wary of buying it used, not knowing how previous owners have treated it and how much wear it has on it, particularly if there's no warranty.)
As to your question, either of those Canon lenses set to 15mm should give virtually identical angle of view as your 15-85mm when it's zoomed to 15mm. There may be slight variance just from the way focal lengths get rounded off, but not enough to make any real difference. Focal length is focal length, period. Among lenses for crop sensor cameras like yours, focal lengths in the 28mm to 16mm range are "slightly wide" to "moderately wide". Lenses that zoom to the 15mm to 8mm range are often called "very wide" or "ultra wide".
Years ago I did close comparison of a number of ultrawide zooms. There are some newer ones now that I've never tested, but after trying out a five or six I ended up buying a Tokina 12-24mm at that time. Back then there was only the one Canon available (10-22mm) and it was a whole lot more expensive than the Tokina, which I felt came close in performance. I eventually replaced the Tokina with a Canon 10-22mm, when I got a really good deal on one. Today, in my opinion, look no farther than the two Canon lenses above, which are both now very favorably priced. While there are several ultrawides to choose among from Sigma, Tokina and Tamron, in my opinion none of the third party wide angle zooms are particularly competitive with the two Canon lenses listed above. The third party lenses tend to be bigger, not have quite as good image quality (none have as good flare resistance as the Canon), most lack image stabilization (which one of the Canon has), tend to be bigger and heavier, and may even cost more! Yes, there are some third party exceptions. For example Sigma offers an 8-16mm that's the widest non-fisheye lens available from anyone. Tokina offers a couple f/2.8 and f/4 lenses without variable aperture. But for landscape photography in particular, those are rarely necessary. Most often landscape shooters are stopping down to a middle aperture anyway, such as f/8 or f/11, for sufficient depth of field and maximum fine detail. So a larger aperture lens... which will necessarily be bigger and heavier, possibly more expensive too... may be of limited use for landscape photography. Especially since many landscape photographers choose to use a tripod.
With either of the Canon lenses, I highly recommend getting their matched lens hoods. Those not only shade the lenses from oblique light, they also can physically protect them from bumps while you are out shooting with them. The EW-83E hood for the 10-22mm is rather large (like a small Frisbee!) and the Canon OEM version is rather pricey at around $35. I thought because the lens is one of the best at controlling and avoiding flare, I might get by without carrying it around to use my lens. But I did some comparisons (examples below) and found it definitely served to prevent flare in certain situations. So I made room for it in my camera bag, carry and use it all the time. The EW-73C that's matched for the 10-18mm is both more compact and less expensive ($25). In both cases, there are also less expensive third party "clone" hoods available from manufacturers like Vello. I don't have any experience with them so can't say how good they are... But, hey, a lens hood is a lens hood! (I would avoid the even cheaper "generic" tulip shaped hoods that screw in. Those can rotate too easily, causing vignetting in images.)
Canon EF-S 10-22mm lens
without lens hood:
Canon EF-S 10-22mm lens
with lens hood:
Have fun shopping!
b Canon EF-S 10-18mm f/4.5-5.6 IS STM /b is a lo... (