Thank you for sharing your store link here. I was able to see the party dog button on your store, and while entertaining I can understand your concern if you didn’t intentionally add this yourself!
A few things I can offer to help you track down this errant button:
Reach out to our live support to review recent app changes to your theme file. This will help us narrow down if this is related to a live app on your store, or a code customization. To help with this, please try and confirm the earliest date you or your team noticed this button on the live store.
Try: 1635648604fb06c4e6 (the ID for it when inspected)
Try other unique characters or lines from what we see when inspected.
If you find something, use the comment code boxes to “hide” the code from running to see if that is the culprit:
{% comment %} tag before the code and a {% endcomment %} tag after the code
I did also notice when inspecting your store that there is a lot of broken code, most likely left behind by apps that are no longer installed. After the holiday season it might be worthwhile refreshing your store theme file with a newer version and removing those extra broken scripts.
