Hi nicolefrompully,
The following article has some information that you may find helpful. Specifically the section that has steps for checking mail fetch and notification settings: If you can't receive email on your iPhone, iPad, or iPod touch.
Check Mail Fetch and Notification settings
By default, Fetch New Data settings are based on what's provided by your email service. If Push isn't available as a setting, your account will default to Fetch. These settings affect how your device receives email. To adjust these settings:
1. Go to Settings > Mail, then tap Accounts.
2. Tap Fetch New Data.
3. Choose a setting — like Automatically or Manually — or choose a schedule for how often the Mail app fetches data.
With iOS 11 and later, and iPadOS, Automatically is set by default. Your device will fetch new data in the background only when your device is charging and connected to Wi-Fi.
Make sure that your Notification settings are correct for the Mail app:
1. Go to Settings, then tap Notifications.
2. Tap Mail, then tap an email account.
3. Adjust your Alerts, Sounds, and Badges.
You also mentioned not receiving notifications from a third party app. The steps in this resource will help if the app isn't working as expected: If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open.
Cheers.
