Push notifications delayed several minutes

**Describe the bug**
For example, someone sends me a message on WhatsApp, and the notification often arrives 20 or 30 minutes too late.

Sometimes I worry I'm not getting notifications and decide to keep opening WhatsApp all the time to look for new messages. Immediately after opening it, I can see at a glance that the conversation list has no unread messages. One second later, an unread message from 10 minutes ago pops up on top.

I've seen it happen with other apps too; but WhatsApp is the one that gets it the most, due to the high volume of notifications it sends.

It feels like notifications don't arrive while the phone is locked and the app is running on the background. ~It could be related to [this bug](https://gitlab.com/LineageOS/issues/android/-/work_items/9896) I've reported to LineageOS, which causes apps to be killed aggressively by the out-of-memory killer.~ _(EDIT: actually it's not related)_
I'm not sure what's the culprit, so I need your help.

**To Reproduce**
Steps to reproduce the behavior:
1. Install LineageOS (standard, without microG)
2. Install microG Services and Companion from the F-Droid repository (as a normal, unprivileged app). Do the self-check, enable Google Device Registration and Cloud Messaging.
3. Install an app that uses push notifications a lot (e.g. WhatsApp). Test it for a few days. I usually swipe it up (remove) from Recent Apps when I'm not using it.

**Expected behavior**
I was previously on CalyxOS (based on Android 15), which integrates microG as a system app. It was working as expected there.

This makes me think that I should have installed LineageOS from [lineage.microg.org](https://lineage.microg.org/) instead, but I really don't feel like reinstalling everything unless I'm sure it will help.

**System**
Android Version: 16
Custom ROM: LineageOS 23.2
microG Services version: 0.3.13.250932

The report names no source files, tests, or entry points; start by reproducing the delay with Android 16, LineageOS 23.2, and microG Services 0.3.13.250932 while the phone is locked and the app is backgrounded. Compare push delivery before and after opening WhatsApp, and consider the issue done only when the cause is identified and timely notifications can be verified.

Written by the indexing model from the issue text.