It's tough, but I hope you can make it work, because we love having you here!
Big cities are where the good jobs are, but they're also where all the people are, and not nearly enough housing or land area for all of them, so it basically quickly turns into an unaffordable nightmare unless you have generational wealth/inherited property, which of course you won't. Unfortunately it seems this is largely where the default "Canadian immigrant experience" will put you, and it's really not working for anyone as far as I can tell.
I'd argue that you will do better to find yourself a small town to move to that's more remote. Not necessarily somewhere far north or completely outside civilization (although there are many such places in Canada, and in many cases Canadian government will actually give you extra money if you live in these areas as they can be both extremely remote, extreme weather, and extreme cost of basic necessities) But you can find many small less urbanized areas throughout the country, some are farming communities, some are industry towns (lumber, pulp and paper mills, mining, etc) some are better connected and serviced than others, but generally speaking the further away you get from the major cities and capitals, the cheaper housing will be. Other stuff gets more expensive though, but housing is such a dominant cost of living problem right now that it's still the main factor you'll benefit from trying to minimize. Anywhere outside the major cities, jobs will probably suck, but there will be some jobs. They won't be jobs that take advantage of any education you have, they will be simple jobs in hospitality, services, sales, business administration and other less skilled labor that don't necessarily pay very well. Cost of living is much lower in more rural areas of Canada -- depending on how you are willing to live. It can be a harder life, especially if you're used to city life. If you can get some support in the community and are willing to sacrifice some conveniences I think it is probably one of the better and more cost effective ways to live for many people right now. But it's not for everyone, and it may be especially tough for an immigrant as small communities can be insular and isolating. If you can find towns with a Ukrainian diaspora, that would be ideal, and there are already lots of them (and more every day!). Especially in the prairie provinces (Alberta, Saskatchewan, Manitoba) which have long had a significant Ukrainian community well established.
For jobs I'm really not sure what the outlook is for a Ukrainian immigrant. I know there's a lot of bureaucracy and obstacles in getting education and skills recognized over here, which is really a shame. I seem to find a lot of Ukrainian people working in hotels and restaurants for example, because it requires no formal certifications or proof of anything to get such a job, however often these people have extensive education and skills. It's a shame for everyone involved, but a job's a job, and you need a job to pay the bills, so at least there's something. If you can find a way into something like the trades or industry, the money is crazy good and people are desperate to hire right now, but again, the process for getting people trained and certified is long and probably very frustrating.
I don't know what you expectation of standard of living is like. I know Ukraine used to be quite a poor country overall, but I think it was quickly improving before the war, and like Canada, I think there was quite a significant variation between the relatively wealthier cities and the remote rural towns. I think you will find it overall is similar here, although the prices and scales will probably be much different.
Wish you all the luck, and hope you have a great experience here.
All of this is fair, but I want to add some encouragement to consider more remote parts of Canada.
Most Canadians live relatively near the US border and, unless they have travelled, may assume the rest of the country is "uncivilized" -- not so! I have lived for decades in northern regions of Canada in very civilized communities!
I live in Whitehorse, Yukon now -- it is a small city (~30,000+ people), but very liveable, especially if you like outdoor activities and nature. We have all the basic amenities you could wish for (university, library, plenty of stores, trails, recreation, hospital, good restaurants, etc.) and many advantages you might not think of. I can say similar things of other places I have lived and worked in the far north.
Some advantages include sense of community, good access to health care, lots of good employment opportunities, less stressful atmosphere, welcoming people, grassroots politics, travel connections to major cities, natural beauty beyond comprehension, and, for immigrants, much quicker routes to permanent residency. The north is very diverse and surprisingly cosmopolitan, btw -- not all rednecks and yokels.
Northern communities are great places to get established and build up some capital -- even if you eventually decide to move to southern Canada. The north is chock full of people who came up for one summer and loved it so much they never left.
Especially in the territorial capitals, there are many jobs that don't suck! Federal, territorial, First Nations, and local governments, small and large businesses, and non-profits all hire highly educated and specialized workers to high paying jobs with good benefits (and often union membership). If you don't have Canadian credentials in your field, you may find it easier to get a foot in the door in the north.
Yes, the climate here in Whitehorse is cold in the winter, but very comfortable most of the time. We seldom have more than a week or two of unpleasantly cold temperatures (below -10°C) without a break. We also have real summers. Cold might sound terrible, but it really isn't! Yellowknife is the other largish city north of the 60th parallel and is a bit colder, but still very liveable. Similar can be said for lots of other even smaller communities in the territories and northern parts of provinces.
Are there disadvantages? Sure. Cost of living is higher, but so are wages. If you hate winter, you might have to learn to love it. Winter days are shorter further north, but summer days are longer. You have to hop on a plane to visit the big city, but that is not a bug, it's a feature.
Canada is a great place to live, but don't assume you have to live down south. Forgive the analogy, but northern, rural, and remote Canada is the lemmy to Southern Canada's Reddit!