fix: use private field in #castPlayer getter to avoid side effects

[ronald-urbina]

• The #castPlayer getter was calling this.remote (the public getter)
  instead of this.#remote (the private field) to look up the cast player
• this.remote has side effects: it loads the Cast SDK and creates a
  RemotePlayback instance if one doesn't exist yet
• This means every internal property access (paused, muted, volume,
  currentTime, etc.) was potentially triggering Cast SDK initialization
  unintentionally

---

Note

Low Risk
Low risk, one-line internal change that prevents unintended Cast SDK/RemotePlayback initialization during internal property reads.

Overview
Updates the #castPlayer getter in castable-mixin.js to reference the private #remote field instead of the public remote getter, avoiding side effects like loading the Cast framework or creating a RemotePlayback instance during internal state access.

^{Reviewed by Cursor Bugbot for commit 5bb675e. Bugbot is set up for automated code reviews on this repo. Configure here.}

[vercel]

@ronald-urbina is attempting to deploy a commit to the Mux Team on Vercel.

A member of the Team first needs to authorize it.

[snyk-io]

✅ Snyk checks have passed. No issues have been found so far.

Status	Scan Engine	Critical	High	Medium	Low	Total (0)
✅	Open Source Security	0	0	0	0	0 issues
✅	Licenses	0	0	0	0	0 issues

💻 Catch issues earlier using the plugins for VS Code, JetBrains IDEs, Visual Studio, and Eclipse.