15 years ago there was a big court fight about taxing parking, including on street spaces and those in residential buildings. (The question was: can you tax private lots at business rates if competing residential lots are taxed at residential rates and city owned lots, and street parking wasn't taxed at all). I'd imagine a deep dive in the city archives could find some of the reports which flowed through council then.
In 1999 there was also talk of a parking tax, and the city wrote a few reports on it including revenue estimates, which implies at least some knowledge on the number of parking spots. $5 a spot per month was estimated to bring in ~$2.4 million a year.
Here's an interested google success - a strategic report from the Calgary Parking Authority.
https://www.calgaryparking.com/documents/10184/11460/Final+-+10+Year+Strategic+Plan.pdf
On slide 20, the CPA references they have 14% of all paid parking at a supply of 14,357 in 2014. Doing the math, that would suggest they estimated that there was 102,550 paid parking stalls in 2014. The geography is unclear though - likely most would be downtown?
On the next slide they might have calculated it:
So looks like about 45,000 stalls in downtown in 2014. However, it's not clear what that includes (e.g. an apartment/condo that has a stall but dedicated to an owner, does that count in this supply? What if they rent it out? etc.) It also wouldn't include any garages since 2014 - Brookfield Place etc. Painfully, the chart also shows the sparkle in CPA's eye that eventually morphed into the incredibly wasteful Platform garage in East Village.
What's also painfully obvious from this document - the CPA really took that 60/40, transit/private vehicle mode split downtown as the goal,
not greater than 60% transit as the goal. This document reads that they are trying to maintain 40% car mode share. Another classic example of following the letter of the law (60/40 split exactly) but not the spirit (a larger transit mode share is better for a city's health).
Can you imagine if they modelled an economic downturn? A slight bit more nuance from CPA in why we are making mode split goals and a few more realistic demand scenarios (including demand decreases) and we'd probably have saved ourselves $60M and a parkade.