Where can I find a list of job titles that programmers(or/and related specialties) have, e.g. mobile, web, developer, software engineer, co-founder.
For the list of programming languages, for example, I found Stack Exchange Data Dump.
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I would take a short list of programming langauges and then search those terms on a job website.
For example, searching indeed.com for 'python' returns job titles of 'Data Developer', 'Build Automation Engineer', 'Software Engineer - Data Infrastructure', and 31502 more.
I mention indeed.com because they have an API that you can use code to perform searches - LINK. You have to register to get the key, but it's free.
Once you've collected the thousands of job titles (and summary, descriptions, location, etc) for each programming language, you can do some basic stats to see which job titles are showing up most commonly (maybe the top 20 or something).