To display a Mastodon conversation thread on your blog or web page get your embed link from the Mastodon embed code like this.
Click the three button menu on your post.
Click Embed.
Click the Embed code and hit Ctrl-C to copy it to the clipboard.
Paste it into the address bar or a text editor by hitting Ctrl-V.
Copy from http all the way to the end of the long number.
One of my embed links looks like this.
https://gamerplus.org/@hairylarry/113392918262050705
Paste that into the box below.