Class C Rocky Mountains ??

Think I would only use cruise control on the flat and moderate terrain roads, for hilly/mountainous areas I'd put the transmission in tow mode and on downhill stretches make sure you're not using the brakes very much. I think that travel is still limited from USA to Canada and vice versa, but you will have to determine what is allowed now. It's been awhile since we camped in the Banff and Jasper locale, so will defer to other respondents for up-to-date advice; it certainly is beautiful country though and well worth the trip.

I use cruise on flat roads without a headwind. On rolling terrain or in the mountains I use tow/haul. Watch your transmission and water temperatures. Stop and "cool off" if high. You are over thinking this. Go...have fun...sounds like a great trip.

I'll assume this is for a future trip. Border is still closed.
You're probably over thinking it.
Not knowing exactly (year/make/model) what you're driving or pulling, I would have the brakes, transmission, and cooling systems serviced before heading out, and change the engine oil before tackling any major uphill grades. As far as the actual driving, you'll figure it out. I find that down hill grades can be a little more challenging, and it's better to down shift early, than to risk losing control. 4-way flashers are a must when going much slower up hill and down.

Stick it in tow/haul mode (practically) all the time; you have a heavy load all the time. If I'm not mistaken, tow/haul will automatically downshift when descending, but if it doesn't, do so manually to use engine braking for long descents.

Cruise control you'll figure out. It often doesn't work too well in hills and even worse on long grades where it can't come close to maintaining speed (going up) or doesn't know enough to slow down (for the downhill).

When you get a chance (after the borders are reopened), definitely take the trip along the ice fields parkway, and plan on camping along the way. It's a phenomenal road, and if you have the time there's plenty to see and enjoy to fill a few days. Reservations for campgrounds are highly recommended if you want to avoid having to dry camp in the overflow areas.

We've traveled all across Canada in our 30ft Class C towing a Saturn. On one tour we headed west thru Northern Ontario, Winnipeg, Regina, Calgary and then toured Banff, Lake Louise and Jasper. We then traveled over the Rockies to Vancouver. Headed south over the border then back ease from Seattle, Yellowstone, back over the Rockies and eventually home. A lot of big mountain passes. Used Cruise Control when I could but generally not when climbing the big ones. Used Tow mode on occasion.
Class C was on the Ford V10 chassis, no issues at all. We just took our time on the big climbs.
Make sure you book into appropriate RV parks ahead of time. Tunnel Mountain in Banff is great.

Looks like the last couple responses covered everything. We've gone from Banff to Jasper in each of the last 2 summers and our 31' did fine, once pulling a Honda Accord on a dolly.

You'll see all kinds of rigs doing that run. I use cruise when I can but it usually doesn't shift when I want it to, so it's generally in tow mode on hills- going up and down. Much of the road is 2 lane, so you'll want to watch for cars passing you at speed when it's only 1.

There are plenty of sights, like Athabasca Falls and you can dry camp at the Icefields visitor center as many do. We budgeted 6 hours for what Google maps called 3.5 hrs, and it took all day including pictures at pullouts and spending time at the 2 places mentioned.

There are very few roads but it's beautiful scenery. Unless you want to see Valemount via Jasper, you have to go to Revelstoke from Lake Louise to go further west. We went to Alaska via Grand Prairie and returned Prince George, Kamloops to Kelowna - so I assume you'd get to Hope via Vernon - beautiful and challenging with the truck traffic, but not as bad as the tv series Highway Thru Hell depicts since you'll go in summery weather. But there's plenty of traffic of all sizes. Feel free to DM your questions.

Owners manual. Start there.