I’m not a Nest user, but as no one has answered your post, here are some generic troubleshooting tips:
We should first determine whether your problem is provisioning (can’t configure the controller with the Nest’s SSID and password), or an incompatibility between Rachio and your present Nest settings.
When you first set up the new system, did you shut down the old one and configure the new with the same SSID and password? If so, did your other devices connect without doing anything, or with just a simple reboot? If so, did you try just power cycling the controller? If so, we can be confident that this is not a provisioning issue.
Otherwise, see whether you can successfully connect the controller to something other than Nest. This is usually easiest with two mobile devices. Set up one as a temporary mobile hotspot and use the other to run the Rachio app. If this is successful, your issue is not related to provisioning. Otherwise, post details of what happens when you attempt to provision (light codes, app error messages, mobile devices tried, etc.)
Assuming it’s not a provisioning issue:
If you haven’t already done so, set up bridge mode; see Bridge mode - Android - Google Nest Help .
Try disabling DNS rebinding protection; see DNS rebinding protection - Google Nest Help .
Try (as a test) disabling 5 GHz.
If you still have trouble, please post:
Modem make/model? In bridge mode?
Separate router/firewall, if any?
Any access points other than Google Nest, if any?
Which and how many nest Wi-Fi devices? Any special settings?