I have fabric-installer-0.6.1.45 installed.

• When launching with no mods, I can see the connection status of multiplayer servers and can connect to them as expected.
• When I enable fabric-api-0.17.2+build.396-1.16, none of my saved multiplayer servers can be connected to.

Well probably need more information in order to do anything, like version of fabric api and mod list.

Closing since this is not an issue with Fabric API and lack of feedback. If you need further assistance, please join the Fabric discord https://discord.gg/v6v4pMv

Seems like a network issue from what I see, check your Antivirus and Firewall settings.