Internet connection not working only for specific applications

The network issue must be very upstream.

It's possible. Here are a few fundamental troubleshooting steps that may help. Much of the information will be redundant but review everything to determine if there is something you may have overlooked.

• Safari is slow, stops responding, quits unexpectedly, or has other issues - Apple Support
• If Safari doesn't load a page or webpage items are missing - Apple Support
• How to use Internet plug-ins in Safari for Mac - Apple Support
• "Safe Mode": Use safe mode to isolate issues with your Mac - Apple Support. Determine if the problems exist in Safe Mode. Then, restart normally.

If you don't get anywhere, you can use the following procedure to determine if the problem is internal or external to your Mac. Causes may involve your router, your ISP, the DNS Server(s) it uses, or certain user-configurable options.

1. Shut down your Mac.
2. Load macOS Recovery by holding ⌘ and r (two fingers) while you start your Mac with a third finger.
3. At the macOS Utilities screen, release those two fingers.
4. Choose Get Help Online.
5. Safari will launch, but it will lack your bookmarks, favorites, history and other preferences.

Determine if the problem persists while using Safari in that mode. After that, restart your Mac normally, and reply with your observations.

At your option you can also use Terminal while in Recovery mode. Choose Terminal from the macOS Utilities screen, Utilities menu.

Back up your Mac prior to making any changes to its file system. To learn how to use Time Machine please read How to use Time Machine to back up or restore your Mac - Apple Support.

Needless to say, if you are using any non-Apple "anti-virus", "cleaning", or "Internet security" products including "banking security", anything at all in that broad category of utterly useless garbage, don't. A lot of things won't work if you do.