It is demonstrably true that life on a planet alters the conditions of the planet (which then alters the life, etc). Most glaring is the abundance of oxygen in our atmosphere. We don't look for oxygen on other planets because oxygen is necessary for life; we look for oxygen because it's unlikely to exist in high densities without life to produce it.
The sci-fi novel Death's End by Cixin Liu (third in a series) further suggests that life alters the universe rather than just local systems, which was a fun idea. He's a rather long-winded author, but he's easy to forgive.
That said, this is the first time I'm hearing of the hypothesis by name, so I can't be sure what all it says. A quick skim lines up with reality though.
I believe pets are counted as livestock, but it's not specifically referenced as far as I have the interest to read.
https://www.pnas.org/doi/10.1073/pnas.1711842115