For anyone who comes across this, I got it to work. I had to update my version of Plex, but I specifically updated it to the version that was released just before the latest version of ErsatzTV.
So "ErsatzTV Version 25.1.0" was released on January 10th with release notes of (copy/pasting from the release notes here): "Fix synchronizing Plex collections. If this breaks collection sync for you, you will need to update your Plex server"
So I went to the Plex release notes and checked what the last version of Plex to release before ErsatzTV published the latest update and found that on December 17th, 2024 Plex released version: "1.41.3.9314"
Then I made my way over to https://github.com/axlecrusher/plex_download_urls (which has all the historical links to all previous Plex builds) and updated my Plex server to that version.
Now when I click the "sync" button on "External Collections" next to Plex, I get no errors. Nothing shows up after it's finished, but now the "tag" search works perfectly. I use Kometa to create dynamic collections automatically within Plex, so for example "Popular" movies is constantly changing, and I like to have the "best of [insert decade here]" movies, and so on.
I'm able to create smart collections using tag searches like this now:
tag:"imdb popular"
tag:"best of 2023"
So "tag" followed by the exact collection name, in quotes.
And the search results are a 1 for 1 replica of each of the dynamically created collections in Plex.