[Bug]: Loading playlist with unavailable videos using Invidious backend breaks FreeTube

### Guidelines

- [x] I have encountered this bug in the [latest release of FreeTube](https://github.com/FreeTubeApp/FreeTube/releases).
- [x] I have encountered this bug in the [official downloads of FreeTube](https://github.com/FreeTubeApp/FreeTube#official-downloads). **The only official downloads are from the [https://freetubeapp.io](https://freetubeapp.io/#download) website, the [FreeTubeApp/FreeTube GitHub repository](https://github.com/FreeTubeApp/FreeTube/releases) and the [io.freetubeapp.FreeTube flatpak](https://flathub.org/en/apps/io.freetubeapp.FreeTube) from Flathub.**
- [x] I have [searched the issue tracker for **open and closed** issues](https://github.com/FreeTubeApp/FreeTube/issues?q=is%3Aissue+sort%3Arelevance-desc) that are similar to the bug report I want to file, without success.
- [x] I have searched the [documentation](https://docs.freetubeapp.io/) for information that matches the description of the bug I want to file, without success.
- [x] This issue contains only one bug.
- [x] I have read and agree to follow the [rules](https://docs.freetubeapp.io/community/rules/).

### Describe the bug

1. Set `Preferred API Backend` to `Invidiou API`
2. Set a valid `Current Invidious Instance`
3. Go to https://youtube.com/playlist?list=PLvMVt4c68EeXRV2R1fdieei9HwpuUKXKL
4. Scroll down until thumbails no longer load
5. Try to perform any other action in FreeTube (performing a search, going to a channel, a video...)
6. Observe that nothing loads

https://github.com/user-attachments/assets/edf5ac96-6bca-480c-a3c1-825db261dac0

### Expected Behavior

FreeTube should continue to work normally

### Issue Labels

content not loading

### FreeTube Version

v0.25.1-beta

### Operating System Version

Bazzite

### Installation Method

Flathub

### Primary API used

Invidious API

### Last Known Working FreeTube Version (If Any)

_No response_

### Upload screenshots or videos

_No response_

### Additional Information

Reproducing the bug with `Thumbnail Preference` setting set to `Hidden` does not break. This seems to indicate that it's the thumbnails that are causing the bug.

When FreeTube breaks, the Invidious instance still responds to API requests made outside of FreeTube (curl, browser...). This seems to indicate that it's an issue with FreeTube more than Invidious.

### Nightly Build

- [ ] I have encountered this bug in the latest **official** [nightly build](https://docs.freetubeapp.io/development/nightly-builds), do not check this box if you are using an unofficial or custom build.

Reproduce the failure with the linked playlist, the Invidious backend, and thumbnails enabled; compare it with Thumbnail Preference set to Hidden. Start by tracing playlist thumbnail loading and the point where later searches or channel and video navigation stop responding. Done means unavailable playlist videos no longer break subsequent FreeTube actions.

Written by the indexing model from the issue text.