Even in macOS 15.5, Safari uses sometimes Aqua-styled controls for e.g. dropdown menus. I wonder if this been fixed in macOS 26? Tried it on the site https://calendar.online/ and create a demo live calendar and look at the settings.
I just tried it with Firefox, Chrome and Safari. While Safari matched your screenshot, both Firefox and Chrome used a flatter look for the same elements. This might be less of a Safari issue and more of a backend/coding issue though depending on what was used to define the button styles.
My guess is, that those controls are coming from the browser, yes, there are CSS settings but I see them on several websites and it looks even worse in dark mode. Apple could fix it but doesn't. :-(