To stay mobile, and also avoid the expensive cost of rent, can you live in a Caravan for a long term? or even permanently?
Some people live in caravans (or trailer homes as they are known in the US), sometimes for long periods of time, as a matter of necessity due to their economic situation. Most people find such a living arrangements unsatisfactory. In addition to social stigma associated with this style of living, most people dislike to lack of permanency.
Other issues involve the requirement for personal hygiene facilities: bathing, ablutions, laundry facilities for clothing & bedding. As well as limited space for a kitchen pantry and refrigerator.
Edit - Additional material.
Depending on the location, some caravan parks allow people to stay for lengthy periods of time, others only allow people to stay for a limited amount of time before having to move elsewhere. Some of the reasons for limited tenure is to clear the park for the local tourist or holiday season. Which can be a lucrative time for caravan park owners and also because some customers are regular temporary customers during such periods.
This recent news item (12 June 2022) illustrates what some people are prepared to due, with years of planning, to be able to live a nomadic lifestyle in a specially commissioned off grid caravan.
It is not for everyone, and even if it agrees with you, it may not be for you for a very long time. That said, I'd plan for a fixed period, after which you could choose to extend, or abort.
I lived on a bicycle for over a year! My only possessions were what could be carried on the bicycle. I slept under highway overpasses quite often. I would occasionally hire a room for a month or a few, to get me through the winter, or so I could make some money in order to continue.
I have a step-daughter who loves the vagabond life-style. As I recall, her primary motivation was the high cost of rent. She has a 26' motor home, and pulls a trailer that hauls a motorcycle. She's a phlebotomist (blood drawer), who does contract work. When a contract is nearing its end, she can renew if she likes where she is, or look for another contract somewhere else. I don't know how she makes her parking arrangements, but I know she almost never stays in organized campgrounds. Most places where she works have employee shower facilities. She generally avoids putting anything in the blackwater tank, unless "on the road" instead of parked somewhere.
Providing for your income may be difficult if you don't have a "portable" career, though. Even with a conventionally portable gig, like remote work, maintaining a reliable Internet connection may be difficult.
So it certainly is possible, with some compromises and sacrifices.
In Canada, you'll have to either flee to the West Coast for the winter, or put some serious thought into how to make it through the winter. Most motor homes are not designed for over-winter occupancy, with requirements to drain your fluids and bring your deep-cycle battery indoors, for example. And if you do choose to heat it over the winter, keep in mind that they typically are not insulated well, and you may be spending a lot of fuel, just to have it go through the walls and ceiling!
Legally, everything is going to depend on the jurisdiction. On Salt Spring Island, there are places where the authorities simply turn a blind eye to, and there are caravans parked there most of the summer, and well into the colder months. Take time to talk to other such campers, who will share with you where there are good places to stay, and where to avoid.
I'm not sure what this has to do with "sustainable living," though! I think people living in campers may well use more resources than someone staying on even a small plot of land where they can supply at least some of their own food.
I had great fun while being a vagabond, but it eventually got old. "Normal" things like having a family, or having a typical "career advancement" can be a challenge. But if that is not a problem for you, go for it!