No, they do not get access unless you allow it and explicitly selet a bluetooth device the page is allowed to connect to. The bluetooth dialog is handled entirely by the browser.
PWAs don't have one of the major downsides of Electron, which is bloat - you don't have to package the huge runtime yourself.
That aside, sure, I'll always take a native app if I can have it. But providing native apps across all major desktop and mobile platforms is a lot of effort, especially for small businesses and hobbyists. In that case, a PWA is vastly better than nothing at all, or a native app for one particular platform that just happens to be the one you don't use.