Test in screen readers and see how content is being announced.

Lists have certain semantics which are very useful. Definitely good in navigation (aka nav > ul > li).

Grids are also useful BTW—we don't have specific "grid" tags in HTML, but using ARIA attributes you can set up grids which might map onto div tags or even custom elements.

Personally, I'm much less concerned about ul/li than I am "div tag soup" which is a plague upon modern web development. Use div tags sparingly, and almost always see if you can reach for either (a) a more semantic HTML tag (e.g., key/val pairs should probably be dl/dt/dd tags, not list tags), or (b) custom elements…yes, authoring tags with one or more hyphens which are purely for developer comprehension and hanging CSS off of is perfectly fine—recommended in fact—and in some cases if you need some JS component logic as well, then boom you have web components.

I would refer to MDN documents on whatever features you are attempting. eg:

• Navigation: https://developer.mozilla.org/en-US/docs/Web/HTML/Element/nav
• Forms: https://developer.mozilla.org/en-US/docs/Web/HTML/Element/form

The general term you are looking for is 'Semantic HTML' i.e. the tags convey their purpose/meaning.

• https://www.semrush.com/blog/semantic-html5-guide
• https://developer.mozilla.org/en-US/curriculum/core/semantic-html

HTML is open, you could easily scrape websites and generate some stats about how often they're used.

But no, ul and ol are for exactly what you'd expect them to be used for.

Incidentally the Mozilla docs for ol say:

Unless the type of the list number matters (like legal or technical documents where items are referenced by their number/letter), use the CSS list-style-type property instead.

This is an old standard, long ago when CSS wasn't a big thing, and even when it was when it was much less featureful, tables where the only way to properly position things. This is no-longer the case and is now bad practice and has been for more than a decade. This is due to defailt styling added to list elements along with a few other issues with speed and consistancy

Don't know them, but this seems an older Dev who learned something one way and is entirely unable to adapt with changing technology. This is a danger, and has been the reason for quite a few major, very expensive, issues at companies I've been contracted at. Sure, using tables and lists is not a big issue, but what else will he do and defend aggressively? I've seen the same with a person arguing SQL injections are fixed because he took out all comment characters before concatenating a string for an SQL query.

It does sound like lists may be a little overused but it would be hard to say without specific examples.

Using lists in the nav situation seems reasonable. But if he's advocating that everything on a web page should be a list, that's a bit extreme.