[bilibili] supporter-only videos broken after 239f5f3
### DO NOT REMOVE OR SKIP THE ISSUE TEMPLATE

- [X] I understand that I will be **blocked** if I *intentionally* remove or skip any mandatory\* field

### Checklist

- [X] I'm reporting that yt-dlp is broken on a **supported** site
- [X] I've verified that I have **updated yt-dlp to nightly or master** ([update instructions](https://github.com/yt-dlp/yt-dlp#update-channels))
- [X] I've checked that all provided URLs are playable in a browser with the same IP and same login details
- [X] I've checked that all URLs and arguments with special characters are [properly quoted or escaped](https://github.com/yt-dlp/yt-dlp/wiki/FAQ#video-url-contains-an-ampersand--and-im-getting-some-strange-output-1-2839-or-v-is-not-recognized-as-an-internal-or-external-command)
- [X] I've searched [known issues](https://github.com/yt-dlp/yt-dlp/issues/3766) and the [bugtracker](https://github.com/yt-dlp/yt-dlp/issues?q=) for similar issues **including closed ones**. DO NOT post duplicates
- [X] I've read the [guidelines for opening an issue](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#opening-an-issue)
- [ ] I've read about [sharing account credentials](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#are-you-willing-to-share-account-details-if-needed) and I'm willing to share it if required

### Region

CN

### Provide a description that is worded well enough to be understood

[account-needed]
after 239f5f3 , yt-dlp raises an `ExtractorError` on every supporter-only video regardless of whether the user has logged in as a supporter. But I don't have a supporter's account. An account with access to _any_ supporter-only video on the site would help

### Provide verbose output that clearly demonstrates the problem

- [X] Run **your** yt-dlp command with **-vU** flag added (`yt-dlp -vU <your command line>`)
- [ ] If using API, add `'verbose': True` to `YoutubeDL` params instead
- [X] Copy the WHOLE output (starting with `[debug] Command-line config`) and insert it below

### Complete Verbose Output

```shell
[debug] Command-line config: ['--test', 'https://www.bilibili.com/video/BV1jL41167ZG/', '-vF', '--no-simulate']
[debug] Encodings: locale UTF-8, fs utf-8, pref UTF-8, out utf-8, error utf-8, screen utf-8
[debug] yt-dlp version stable@2024.11.18 from yt-dlp/yt-dlp [7ea278792] (source)
[debug] Lazy loading extractors is disabled
[debug] Git HEAD: 62cba8a1b
[debug] Python 3.13.0 (CPython x86_64 64bit) - Linux-5.15.167.4-microsoft-standard-WSL2-x86_64-with-glibc2.35 (OpenSSL 3.0.2 15 Mar 2022, glibc 2.35)
[debug] exe versions: ffmpeg 4.4.2 (setts), ffprobe 4.4.2
[debug] Optional libraries: Cryptodome-3.21.0, brotli-1.1.0, certifi-2024.08.30, curl_cffi-0.7.1, mutagen-1.47.0, requests-2.32.3, secretstorage-3.3.3, sqlite3-3.37.2, urllib3-2.2.3, websockets-13.1
[debug] Proxy map: {}
[debug] Request Handlers: urllib, requests, websockets, curl_cffi
[debug] Loaded 1837 extractors
[BiliBili] Extracting URL: https://www.bilibili.com/video/BV1jL41167ZG/
[BiliBili] 1jL41167ZG: Downloading webpage
ERROR: [BiliBili] 1jL41167ZG: This is a supporter-only video: 该视频为「高级充电回馈」专属视频，开通「18元档包月充电」即可观看. Use --cookies-from-browser or --cookies for the authentication. See  https://github.com/yt-dlp/yt-dlp/wiki/FAQ#how-do-i-pass-cookies-to-yt-dlp  for how to manually pass cookies
  File "/home/user/yt-dlp_dev/yt-dlp-fork/yt_dlp/extractor/common.py", line 742, in extract
    ie_result = self._real_extract(url)
  File "/home/user/yt-dlp_dev/yt-dlp-fork/yt_dlp/extractor/bilibili.py", line 657, in _real_extract
    raise ExtractorError(
    ...<2 lines>...
        f'{self._login_hint()}', expected=True)
```