Plugin update notifications are generated by making a communication connection to the WordPress plugin API server (wordpress.org) to perform a check for any new plugin versions. So it sounds like either something that you have installed (plugin or theme) is interfering with that communication or something installed on your web host server is interfering with that communication. Most likely one of the plugins you have installed is improperly doing an API server plugin upgrade check, which is breaking all other API server upgrade checks. It could also be your theme. What you need to do is standard WordPress plugin and theme troubleshooting. Switch your theme temporarily to the WordPress twentytwentyone theme (or another WP theme) test/check things. If your theme is not causing the problem then deactivate your plugins 1 by 1 until you find the plugin that is causing the problem.
Start with premium/paid plugins since it is most likely that 1 of your premium/paid plugins is causing this problem.