I'll admit, sometimes this makes some sense; you may be building an interaction that doesn't map cleanly onto either "trigger action" or "show information", and you wish to pick and choose the semantics that best fit your needs.
...But then there's the situation you allude to, where you have a button (action) and a link (navigation) and are just trying to make them look the same for consistency. Even if you pull it off visually, the chance that an end-user's client software will misinterpret what you're doing in some way and cause confusion is high.
But I guess the main point is not to use buttons in your nav bar.
1) Can you return things to exactly the state they were before simply by hitting the browser's "back" button once? Then use a link. Otherwise use a button.
2) Will this navigation have side effects (eg, change values in the DB)? If so, then use a button. Otherwise, use a link.
<form> <button formaction="https://your/destination">Clicky!</button> </form>
In real life there are 100 times as many accessibility problems as on any web page – why shouldn't they be sued?
We are sometimes told not to use a button when a link will do [1]. Supposedly, links are better for accessibility or for user expectations. You can style links to look like buttons, but I have trouble making them exactly the same if they’re next to each other (for example, the same height) and it seems like doing it the hard way.
So how seriously should I take that advice?
[1] https://www.a11y-101.com/design/button-vs-link