For some reason, I'm trying to use tags that are not included in HTML tags, for example
<new_tag>This is new to html</new_tag> Everything seems to work as I wanted across all browsers, but is there any SEO consequence on this?
Without additional context, it's difficult to give you a concise answer to your question. It would be helpful to know more about these custom tags you're using, how they're implemented, and how they are ultimately rendered onto the page.
Assuming your custom tags are implemented using the Web Components API (a rather big assumption...), I don't think there should be any impact to SEO. Web Components are implemented through a shadow DOM but ultimately get attached to a "shadow host", which is a regular DOM element recognizable by all browsers (and crawlers, etc.).
So for example, if your
<new_tag> is implemented via an
h1 DOM element, it would ultimately be rendered as an
h1 and can then be detected as usual for SEO (or accessibility) purposes.
I'd suggest implementing your custom element(s), then inspect the page in the browser (F12 to access Chrome DevTools) and see how it gets rendered in the HTML.
Google has long said that they care more about pages working for users than meeting standards. As long as your pages work in all widely used browsers, using non-standard tags should not be a big issue for SEO.
In fact, with a few exceptions, Google doesn't seem to care what tags you use at all. Pages seem to rank well regardless of how they are implemented in the source code. Page content and presentation to users matters a lot more than tag choice.
The tags that actually matter for SEO are:
<title>— Very important to write a good title in title tags for SEO
<meta>— not all matter, but some do
<link>— canonical tags, maybe some others
<a>— link your pages to make your site crawlable
<img>— for image search
<h2>, etc. — maybe matter these days
Beyond that, I wouldn't worry much about using or not using various tags for SEO.