Im not familiar with tools like this, but one thing you can do is include a unique hashtag for your posts and after like 20 mins go check other instances for your hashtag to see if your post federated
I do this a little from time to time, but not only because I want to see if my posts federated, but also because I want to see if there's posts I have not federated with on my instance that I would like to connect with
I havent done this, but a way to do this is create a bookmark folder on your browser, and go to multiple instances on joinmastodon.org
On those servers, go to your hashtag URL
Bookmark each server with this
Example with #cats:
https://mastodon.social/tags/cats
Once you have all of these in a bookmarks folder, whenever you want to check them all at once, hit the folder with your middle mouse button and it should open them all at once, then take a look around!