I want to share my experience. Truly, Canada, UK, USA, Australia and New Zealand share immigration information among themselves, but not in all visa applications.
I applied for a UK student visa via an agent in 2013. The agent used a forged account, and the application was refused with a 10 years ban. The agent went ahead to falsify the letter by removing the part that specified that a fake account was used. He then gave me the falsified letter. I only thought I was refused a visa, I never knew I was banned.
In 2016, I applied for a New Zealand tourist visa. In the form, I stated I was refused UK visa in 2013. New Zealand issued me a tourist visa. In 2019 I applied for a Schengen visa and it was issued.
In 2021 I applied to visit the UK, the application was refused, they stated that I used a fake account in 2013,and I was banned for 10 years and the ban will expire in 2023. That was how I got to know that I was banned. If I had known about the ban, I would not have applied at all.
My point is, these embassies don't have luxury of time to be wasting on mere tourist and students visas, and they operate different immigration rules. They use the same database which will show to them if the applicant has committed a crime in any of the 5 eyes countries. They are majorly concerned about whether you have a criminal records with any of them, and once you are honest about the past refusals, you are good to go.
Immigration files of individual applications are highly voluminous, and all immigration officers are very limited to time, hence, they can't be going through your UK files while processing your Canada study visa. So my advice is: just state your past refusal, that's all, as long as you have never committed a crime, then, you are good to go.