I have marked all my notifications as read and the notification is still there

All your emails may not have been downloaded yet based on your Push / Fetch settings. The notification badge which you see is from the email client server.

Which email account are you referring to? Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

You may know that there are two settings (Fetch and Push Mails). What have you set? Watch the GIF below

Google, AOL, Yahoo - Only Fetch mail Option is available

iCloud, Exchange, Outlook - Both Fetch and Push Mail option is available

1. Push Mail: Whenever possible the email client will push mails to all your devices.
2. Fetch Mail: You need to set How you want it to be fetched, Automatically, Manually , Hourly,Every 30 mins, every 15 mins
   1. Automatically: will fetch when the iPhone is powered and on WiFi
   2. Manually: with fetch when you open email, open Inbox and swipe down
   3. You get an email notification as soon as the client server receives an email and your device is connected to internet, irrespective of whether the mail is in your device's Inbox or not

For the second part of your post; probably you have bought iCloud storage which has nothing to do with iPhone storage or email.

I have noticed that since upgrading to IOS 13.5.1, mail notifications will not show marked as read no matter how long I give them to disappear. I didn't have this issue pre update. What I have to do is close the mail app and reopen it to ensure the read notification alerts are no longer there. I know that doesn't help you with your issue but just wanted to add comments to this thread.