Repository: flutter
Issue: [video_player] Some subtitles in VTT file are skipped
Labels: p: video_player,package,team-ecosystem,has reproducible steps,P2,triaged-ecosystem,found in release: 3.20,found in release: 3.21

### Steps to reproduce

1. Download any VTT file (I'm using the one from Avengers end game as a test)
2. use setClosedCaptionFile on an already initialized video controller to set the file content
3. add a listener to the controller that prints the `controller.value.caption.text` at each call (and, obviously, also if it is included on a widget)
4. Notice that some lines are completely skipped even if present in the vtt

### Expected results

All of the lines should be displayed and non should be skipped

### Actual results
```
WEBVTT

00:07.174 --> 00:09.842
BARTON: Okay, hold on,                                     <-------- Skipped
don't shoot.

00:10.928 --> 00:12.679
- You see where you're going?,                             <-------- Skipped
- Mm-hmm.,                                                 <-------- Skipped

00:12.846 --> 00:13.846
Okay.

00:14.014 --> 00:15.932
Now, let's worry,                                          <-------- Skipped
about how you get there.

00:16.809 --> 00:18.184
Gotta move your foot here.,                                <-------- Skipped

00:18.686 --> 00:20.103
Point your toe this way.

00:20.479 --> 00:22.021
Your hips here.
```
and so on

### Code sample

doesn't apply as the setup to reach the bug is pretty complicated

### Screenshots or Video

_No response_

### Logs

_No response_

### Flutter Doctor output

flutter doctor -v
[✓] Flutter (Channel stable, 3.16.9, on Microsoft Windows [Versione 10.0.19045.4046], locale it-IT)
    • Flutter version 3.16.9 on channel stable at C:\flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 41456452f2 (6 weeks ago), 2024-01-25 10:06:23 -0800
    • Engine revision f40e976bed
    • Dart version 3.2.6
    • DevTools version 2.28.5

[✓] Windows Version (Installed version of Windows is version 10 or higher)

[!] Android toolchain - develop for Android devices (Android SDK version 33.0.2)
    • Android SDK at C:\Users\bonfr\AppData\Local\Android\sdk
    • Platform android-34, build-tools 33.0.2
    • Java binary at: C:\Program Files\Android\Android Studio\jre\bin\java
    • Java version OpenJDK Runtime Environment (build 11.0.13+0-b1751.21-8125866)
    ✗ Android license status unknown.
      Run `flutter doctor --android-licenses` to accept the SDK licenses.
      See https://flutter.dev/docs/get-started/install/windows#android-setup for more details.

[✓] Chrome - develop for the web
    • Chrome at C:\Program Files\Google\Chrome\Application\chrome.exe

[✓] Visual Studio - develop Windows apps (Visual Studio Community 2022 17.8.0)
    • Visual Studio at C:\Program Files\Microsoft Visual Studio\2022\Community
    • Visual Studio Community 2022 version 17.8.34309.116
    • Windows 10 SDK version 10.0.22621.0

[✓] Android Studio (version 2021.3)
    • Android Studio at C:\Program Files\Android\Android Studio
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.13+0-b1751.21-8125866)

[✓] Connected device (3 available)
    • Windows (desktop) • windows • windows-x64    • Microsoft Windows [Versione 10.0.19045.4046]
    • Chrome (web)      • chrome  • web-javascript • Google Chrome 122.0.6261.94
    • Edge (web)        • edge    • web-javascript • Microsoft Edge 122.0.2365.66

[✓] Network resources
    • All expected network resources are available.

! Doctor found issues in 1 category.

# PS:
I noticed a similar issue was also opened but I think it was erroneously closed so i opened this new one (#123796)