Chromecast: Progress Is Not Tracked Even if Keep Screen Awake Is Enabled

### Description

Reported in #7641655-zen:

> When casting to Chromecast audio devices, [...] I'll connect to a Chromecast group, start casting audio, and then forget about it for a while. But if I go back to pause/fast forward/rewind the podcast, and Pocket Casts has been in the background for a while, it's totally out of sync with the current progress of the podcast, like it forgot to keep track of progress when it went in the background several minutes ago.

Initially, we thought that this might be the known issue with progress not being tracked when casting. The workaround for that issue is to enable "Keep Screen Awake." However, the "Keep Screen Awake" didn't make a difference for the user.

### Step-by-step reproduction instructions

So far, we have been unable to replicate the issue.

Slack discussion: p1707830178207379-slack-C02A333D8LQ

### Screenshots or screen recording

_No response_

### Did you search for existing bug reports?

- [X] I have searched for existing bug reports.

### Device, Operating system, and Pocket Casts app version

Phone: Google - LYNX - Pixel 7a - lynx
Android version: 14 SDK 34
App version : 7.56-rc-2 (9187)

*** User notes that they have been on the latest update of Android 14 for a couple weeks, and they only noticed this problem after their Pocket Casts app was updated to v7.56-rc-2

No files, tests, or entry points are named. Start by reviewing the reproduction details and the linked Slack discussion p1707830178207379-slack-C02A333D8LQ, then investigate Chromecast audio progress tracking while the app is backgrounded. Done means the reported out-of-sync behavior is reproduced and progress remains current after returning to the app.

Written by the indexing model from the issue text.