Hi janetfrommesquite
welcome to the Apple (user-to-user) Community.
Re: "iPhone 13 not connecting to CenturyLink Wi-Fi"
Apple support have articles online that may help:
How to: Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
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Re: "What’s the issue with the iPhone?"
If your phone isn’t working right, try re-starting it: Turn iPhone on or off - Apple Support
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Re: "It tells me that my password is incorrect, but it is not".
Seems like iPhone must still expect the password for your old wi-fi provider
You might want to check carefully through the article below :
Eg: check for any steps that may have been missed in changing providers
What to do: If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support
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More Trouble-shooting if needed:
Recommended settings for Wi-Fi routers and access points - Apple Support
How to: Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support
Check VPN (Virtual Private Network) and third-party software to help resolve network connectivity issues - Apple Support
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More support if needed:
You might want to reach out to iPhone Support:
There's a "Get Support" link (online chat / phone / eMail etc) at the bottom of their website (link below),
iPhone - Official Apple Support
All the best :-)
