Not OP but it would appear that any phone that is out of warranty will be denied a repair or refund.

I've been emailing back and forth with Google support about this issue for the past two weeks, and thusfar the only information I've gotten is that the reason my phone is denied a repair or refund is because the warranty expired in 2024.

I don't even have information on whether my phone contains a defective battery in the first place. Since the refund eligibility tool doesn't say that, and I haven't received an answer to that question yet from support.

Given that the Pixel 4a came out in 2020 and the Pixel 6a in 2022, with warranties generally lasting 2 years, most phones will be out of warranty.

Edit: This is the most recent response I've received from Google Support.
The reason why the terms "eligible" and "impacted" are used like this is because I was trying to figure out the reason for the inconsistencies between the terms on their support page

I am very disappointed with the way Google appears to be handling the issue. They ship their phones with defective batteries, and are now not really doing anything to properly communicate the problem and fix the issue.
Instead we get a mandatory update and no real information

It seems that I qualify for the replacement, I'll follow up more when I have more time.

Fortunately I can keep my phone on my desk charging while I work with headphones on away from the desk.

Sure, if you're willing to walk around with a potential lithium fire hazard in your pocket, that's your choice.