Suppose you want to know what radiologists usually search for. Is there a service that can sell you this data?
I have no experience with SEO, but I suppose that only the company that operates a given search engine has access to search frequencies. There may be exceptions, such as inadvertently running spyware of all kinds, but none that would help us. I was thinking about getting this data from Google.
The main tool to access the Google search data is Google Trends. You can use it to see the top 25 searches for a given time interval, geographic location, category, but not by profession. Also the number of results seems to be limited to 25.
Then there is Google Analytics and Google Search Console. However these tools seem to be designed to help you manage your website, and not do research about your potential visitors.
I am quite surprised that it seems so hard to achieve. However, I learned that when a seemingly trivial endeavor turns out to be very hard, it usually means that things are done differently. If you have any advice, not necessarily Google related and not necessarily answering this question, I would love to hear it.