Bug 212102

Description:
On Video.js we received a report that captions stopped working when entering the native fullscreen on iPhones: https://github.com/videojs/video.js/issues/6640.
At first, I couldn't reproduce it because I originally had an iPhone with 13.3 and an iPad with 13.4.1, but the iPad uses the Fullscreen API to put the Video.js player element into fullscreen, rather than taking the video element to native fullscreen like iPhones do.
When I added a button to call enterFullscreen on the video element, I've started being able to reproduce this. I investigated whether it's something related to how we handle text tracks and moving/re-creating the video element in Video.js but creating a simpler test page without Video.js worked fine. We also haven't touched this piece of Video.js in a long time.
Further, when I then created a reduced test case for a coworker to test on a 13.4.1 iPhone, I ended up using a video with HLS and segmented WebVTT in the HLS, which Video.js doesn't handle at all on iOS.
This seems like a bug that was introduced as part of the 13.1 Safari release (https://webkit.org/blog/10247/new-webkit-features-in-safari-13-1/) and iOS 13.4.1. Unfortunately, not sure what else I can do to track down the issue. If there're changes that we can add to Video.js to prevent this from happening, we can do that.

Sample page:
https://codepen.io/gkatsev/full/ZEbVGWN (may require switching to debug mode from the change view button)

Steps to reproduce:
1. Hit Play
2. Make sure that English SDH caption is selected
3. Play through till captions are supposed to show, for example seconds 15-17, 18-20, 20-21, 21-24
4. In windowed mode confirm that captions are showing up
5. In native fullscreen mode (hit fullscreen on an iPhone, or the separate "webkit fullscreen" button below the player on an iPad) note that the captions don't show up.

Expected:
- Captions show up in both windowed/inline mode and native fullscreen mode.

Actual:
- Captions disappear when switching to native fullscreen mode.
- Captions re-appear when exiting native fullscreen mode