You might be surprised.
I can assure you it happened. And my friend is a 35yo physiotherapist who uses a website on a daily basis to manage her appointments.
I guess what was confusing to her was the fact that it was not just a "simple" website where you would find information (blogs, Wikipedia, whatever). It was something where you would say something and it would respond dynamically.
As a software engineer, we know there's no difference. It's just a few POST endpoints anyway. For a user without technical background? The way I described it sounded like it should be an app.
Now, you would say that these people (35yo) used to use Facebook (and maybe Google meet) and such on desktop. So they should know that many things can be achieved through a browser. But it seems like when thinking about mobile, people think differently. A website that "does something" other than displaying information (which is a weird and blurry definition) must be an app. I'm absolutely sure my friend has never thought it could be possible to use Facebook on through her mobile browser. If you access something with your mobile, it must be through an app.