Because an eTicket can contain coupons for up to 4 flights in it, so each of you only has one ticket. The first coupon for the BKK-TPE flight on Thai and the second coupon for TPE-SFO with EVA.

Beyond that, the fact that EVA's system shows the segments confirmed and has the most recent ticket number is extremely reassuring, as the operating carrier's system is what needs to be correct. It's not unheard of that update messaging regarding segment status/changes gets lost between the two airlines systems at times given they are completely different. At this point getting the WL status resolved in the UA PNR is mostly peace of mind, which without being able to see what exactly the issue is (beyond the segment just showing as waitlisted). its hard for anyone except UA to troubleshoot further. Best advice at this point is you just have to keep trying until you eventually get an agent who knows how to manually confirm the space in the PNR after verifying the OA carrier shows the space confirmed. You might try getting connected with web support as those definitely are more experienced agents (and phrase it as a website issue, "on the United website it shows this flight waitlisted but I see it confirmed with EVA and have a ticket reflecting for that flight, so I'm confused why the website isn't updating").

But again, this is mostly about peace of mind at this point. You need a confirmed reservation and current ticket matching that reservation in the operating carrier's system, which based on what you are reporting, you have.

I personally think extremely unlikely. How would UA cancel the flight if they don't even think it is confirmed? Clearly the segment status code for something on the waitlist is different than a flight that is confirmed, so presumably the cancellation codes to cancel a waitlist should be different than cancelling confirmed space.