Notifications are not shown until the app is opened.

### Description

I have Google Podcasts (GP) and Pocket Casts (PC) installed side by side, cause I want to move to PC from GP, so I set he same subscriptions for both for testing.
I receive GP notifications whenever a new episode is released, but PC keeps silent until I open the app.
I have set the battery optimization to "no restrictions", while strangely GP hase "Battery saver (recommended)" option...
I have also granted the notification permission to the app and turned it on inside the app settings.

### Step-by-step reproduction instructions

1. do not open the app for hours
2. From GP notifications I know that my subscriptions have new episodes, but PC does not notify me
3. open PC after a longer period and the notifications will immediately appear

### 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

Xiaomi 11T Pro
MIUI Global 14.0.14 (TKDEUXM)
Android 13 TKQ1.220829.002
Sec: Nov. 1. 2023
PC v7.52 (9168)

Start by reproducing the issue on the listed Xiaomi 11T Pro, Android 13, and Pocket Casts v7.52 configuration, leaving the app closed until a subscribed episode is released. Trace the app's notification and background-update entry points to determine why notifications appear only after launch. Done means subscribed-episode notifications arrive while the app remains unopened.

Written by the indexing model from the issue text.