Once you enter your server URL and hit the "Share!" button it will try to go to the compose window for your account on that server, under the assumption you're already logged in there in the same browser. Then it will open the bare-bones Compose window, with the page title in the title field and the link in post body. Then you can write whatever else you want, add images, etc. before you post:

One downside is the "Submit" button won't close the pop-up window. It will refresh and show you the submitted post in the full web UI, which will likely be the mobile view in that small pop-up window. If you, as a website owner, don't want that experience for your visitors, you can change the script settings to open the share dialog in a new tab instead of a pop-up window. But I set it to default to a pop-up since that's how ALL the other social media platforms do it when you hit a share button.

I was specifically interested in share buttons you can put on a personal website so visitors to the site can easily share your content to their fedi accounts, not for me to share content to my own fedi accounts.

And I wanted it to look and work as closely as possible to how pressing a Facebook or X/Twitter share button works. Once someone has visited your website and told it to remember their instance they don't have to enter it again, so later when they hit the share button on your site it's as frictionless as sharing to any of the centralized social sites.