Help!

My Telegram app isn’t popping up new message notifications, so I’ve missed lots of important messages.

I’m using an Android phone. I’ve turned on sounds both in the Telegram app and on my system, and notification pop-up permission for Telegram is enabled. Does anyone know how to fix this issue?

you should check if battery optimization is restricting Telegram in the background. Disabling battery optimization for the app and making sure background activity is allowed has fixed this for a lot of people. If that doesn't help, try clearing the app cache or reinstalling Telegram.

may be you active your battery optimization option, And 2nd thing is your mobile phone memory is full then android mobile not showing notification

Android phones on occasion decide to 'bug out' and just stop receiving messages. It has happened to me several times. Check if your phone is up to date. If it is, turn your phone completely off, and on again. If you have, and you still do not receive messages, uninstall the app and reinstall it. These are the basic suggestions any tech advisor will tell you to do before assuming there is a different issue.

I use Yahoo to send me messages to my Whatsapp - the verification code, and the same happens to me now and again. Its annoying when it happens, but eventually it will work.

disable battery optimization for telegram specifically in settings, that's almost always the real culprit on android.
also check if you've got "data saver" restricting background data for the app

That sounds like battery optimization issue. Android sometimes kills notifications if an app constantly wakes up the CPU to check for new notifications. You can either disable battery optimization or clear app cache to see if it works.