Using toot in the sense of tooting your own horn is still an odd decision for posts. It implies that users' posts should be focused on bragging about themselves. At least in my opinion that make for a very annoying social media feed to read through.
It's a reference to the trumpeting sound an elephant/mastodon makes, meant as the equivalent to the 'tweet' a bird such as the one in the old Twitter logo makes.
There's nothing more to it than that: A quirky name based on the chosen logo, following the Twitter example.
I agree it wasn't the best word choice, and I can understand why it has been de-emphasised in favour of 'posts', but the reasoning behind it was logical.
