The easy way to check (on desktop) is to open the Help vault, which uses all the default settings. (The answer is no, the behavior you describe happens with default settings.)
Pin a note, then use the pointer from the developer tools to select the pin icon. Note where its markup is highlighted in the HTML window, then unpin the note. You’ll see that its class changes and an inline style appears: <a class="view-action mod-pin-leaf" aria-label="Pin" style="display: none">.
I don’t know which display property is the right one to revert to, but it looks like you need !important to override the inline style. I found that display: initial!important;works.
This is all in the default theme. Minimal’s markup may differ, but you should be able to use the same approach to work it out.