Use Schema to make site name unambiguous
Google and other search engines are generally very good at parsing pages on a site to determine the site name. But on occasion the site name may be ambiguous;
HTML Semantic tags do more than just allow AI to better understand the content of a website. Search Engines do use these tags as well as other content which can be embedded into the coding such as JSON schema. The semantic vocabulary of JSON schema breaks down the content into pieces of data.
Semantic code is also important for ARIA devices and in user accessibility. ARIA devices can navigate the page based on the semantic meaning of the role for these tags. Semantic tags are useful in the design and coding phase and for maintenance by keeping content organized. It is important that the tags are not directly used as styling tags as doing so creates a conflict between design, the page structure, and the meaning of the semantic tag.
For example the <blockquote> has been wrongfully used as a tag to indent content. Instead do the styling using a CSS rule and apply that class to the block quote, or a div that needs to same appearance.
Specific Use Cases
Breadcrumbs (Semantic ARIA HTML and Schema Example)
Breadcrumbs are an important part of website naviagation. From the semantics viewpoint, breadcrumbs need to be readable by both ARIA devices and search engines. Breadcrumbs are shown to users in search as a more informative element instead of the URL near the site title.
Byline Schema and Publish Date Semantics
The date shown in search needs both Schema and Semantic HTML. The date shown on the page needs to agree with the date within the Schema in order to be shown and Google may elect to not display the date if it has other information suggesting a different date. The byline is used to establish authority for the author, which is used by the E.A.T. algorithm in ranking sites.
Navigational Links in Search
Google has been updating the design and style of its search result pages. Navigational links panel has a variation with navigational links as a snippet in the description.
Review Schema, Google Snippets, and E-E-A-T
Review snippets, and Critical Reviews in the Knowledge panel can be provided using Schema. Google's usage of this information is subject to Google's E-E-A-T evaluation for the site, and page.
Jump to Links Snippet, (TOC in search)
The headline tags where designed to allow a TOC to be automatically generated from a web page, but the headline tags are often misused as a style tag. When headline the tags are correctly used and are linked: A TOC can become a snippet for the search results.
HTML div VS (semantic) section & article tags and SEO
It can be said using HTML section or article tags does not effect search engine ranking. In a nuanced way that is true. But I'll be making the case that HTML section and article tags do or can effect search engine rankings.
Semantic HTML header, main, footer, and aside tags
These tags, (header, main, footer, and aside), can be thought of as the basic web page structure tags, Along with the nav tag which is nuanced enough to have a dedicated page.
Semantic HTML nav Tag
The navigation tag is used by ARIA readers to jump to the navigation sections on a page. Search also takes interest in the navigation as it provides additional details as to the topic of the page that it appears on and provides additional details to the pages that are linked to.