Can I get a SEO penalty when using too many H2 tags (10+) on my article? (I must say that I don't look to spam or rank my content, I really need 10-20 H2 tags on my page)
There will be no negative impact. I used a holistic content strucuture for one of my pages and the Free Tools tell me there are too many H2 . But it doesn't matter in the end because there is an amount of Keywords which rank high. You should ask yourself if your content is strcutured and easy to read for users (and search engines as well).
I have not heard of a penalty for using many heading tags. A phrase in Google SEO starter guide kind of provides an answer: https://developers.google.com/search/docs/beginner/seo-starter-guide#headingtags
Use heading tags where it makes sense. Too many heading tags on a page can make it hard for users to scan the content and determine where one topic ends and another begins.
My view is this: Stop worrying about a penalty. The right way to think would be from the eyes of your readers. The right question is this: Will using heading tags at places you intend to help your readers scan and understand your content better? If yes, there is no one stopping you.