There's been lots of discussion over whether people in hospital with Covid are actually there because they need to be treated for Covid. I found Meaghan Kall's recent twitter thread on the latest PHE update really useful in this regard because they do make a calculation of this number. Kall is a PHE analyst who works on these reports. I know it's England and not Scotland, but it should be fairly similar. Note that this is data specific to the Indian variant of concern, but as that is now the dominant variant, that's probably most cases at this point.
twitter.com/kallmemeg/status/1397987124750782470
The info about cases in hospital is in the caption to the figure of the first tweet in the thread, which I have attached here and copied the relevant text into this post.
Cases with an A&E visit/where presentation to A&E resulted in overnight inpatient hospital admission: At least one attendance within 28 days of positive specimen date; cases where specimen date is the same as or after the date of A&E visit are excluded to help remove cases whose primary cause of admission is not COVID-19 picked up via routine testing in healthcare settings. This underestimates the true number of cases who have attended emergency care due to COVID-19 but avoids overestimation due to asymptomatic people attending emergency care for unrelated conditions; validation of this dataset is being undertaken.
So it looks like 3.6% of cases are resulting in an A&E visit, of which 21.4% are admitted. The data in the table does go back to 1 Feb, but something like 90% of the cases are from May (data not shown here) with a well vaccinated over 65 population. I don't know how similar that is to when we had a mostly unvaccinated population in the autumn, which is what we really need to know! I also don't know whether or not PHE uses this filter for its hospitalization figures that go into the public dashboard. If they do, then it's unlikely that there is a large proportion of people in hospital who are only coincidentally positive for Covid.