H1, H2, H3 are all important to let the search engines know what your post is about and what keywords and related keywords to rank you for, but it is not as important to use your exact keywords in H1 as it used to be.
The Google spiders has gotten a lot smarter and understands what your content is about even if you use synonyms in your titles.
H1 will continue to be important because it helps to crawl the content and decide its relevance and determine what it is about.
H1 tags still have high importance in SEO. They are as important as they used to be. But they can't stand on their own. You need to add decent paragraphs in your blogs to expand on your H1 tags reasonably to boost the importance of H1 tag in SERPs.
H1 or even h2 h3 tags continue to play a significant role in structuring content for both seo and user experience. as far my experience, keep 1 H1 as your title of the content, with long tail keywors and layout your content 2 more h2 in middle. this helps in get best results
H1 tag shows what your website is all about. So it is important for SEO. To rank in Google searches, there are many, many factors and H1 is one of them. Maybe there are factors for ranking that we do not know, only Google knows. If we really knew all the factors, SEO would have been easier for us. Some of the important SEO implementations is important for some SEO experts and not so much for the others. This also shows that we really do not know everything.