trouble signing in

Which operating system do you have?  Make sure your computer meets the minimum CPU & GPU requirements. Most Creative Cloud apps work on:

• Windows 10 versions 21H2, 21H1, 20H2, 2004, and 1909 (LTSB branches are not supported);
• macOS 12 (Monterey), macOS 11 (Big Sur), macOS 10.16 or 10.15 (Catalina)

- https://helpx.adobe.com/creative-cloud/system-requirements.html

1. Open CC Desktop App.
2. Click your Avatar (top right image) > Preferences > General tab > Settings. Select "Always keep Creative Cloud up to date."
3. Click on your Avatar again.
4. Sign-out of Creative Cloud.
5. Close all apps.
6. Restart your computer.
7. Open CC Desktop app.
8. Click your Avatar.
9. Sign-in with your paid ID and password.

Failing that, see this help article about connection errors.

https://helpx.adobe.com/x-productkb/policy-pricing/activation-network-issues.html

That first screen tells you to contact support has me concerned there is a deeper issue and this is not specific to DW.  You might need to contact Adobe to resolve this.  First thing I would try is to log in to CC by the web interface: https://creativecloud.adobe.com and see if that works.  If not you may have to go down the support path and call/contact them.