If it has a USB connection, then try that instead since someone reported that may work.
Have you tried to reboot the laptop to see if that makes any difference? Also try disconnecting all other external devices in case one of them is causing a problem. Try removing the former Bluetooth connection for the Cricut and re-adding it again.
You are not alone with these issues as shown in this Reddit thread, although some people there report their Cricut is working with Sonoma:
https://www.reddit.com/r/cricut/comments/170l8xl/cricut_joy_connection_issues_on_macos_sonoma/
Also seems to be an issue for some with the new iOS 17.x on iPhones & iPads:
Bluetooth connectivity to Cricut Joy mach… - Apple Community
Make sure you have updated to the latest version which is 14.1 or 14.1.1 depending on the exact model of your laptop.
Also, check the Cricut support site for any articles or FAQs which may provide suggestions.
Another two options. Install macOS Ventura into a Virtual Machine so you can utilize your Cricut that way, but I'm not sure if this will work since I don't know how Bluetooth works with macOS in a VM. The second option is to install macOS Ventura into another APFS volume alongside your Sonoma installation. You will need to use Disk Utility to add a new APFS volume to the same hidden Container so that both operating systems share the same storage pool, but will be entirely separate. The latter option requires rebooting the laptop every time you want to use the Cricut and you will need to be careful about your data not getting fragmented running two operating systems. A VM allows you to access the second OS without rebooting....it will be like launching a separate app, but your laptop must have enough resources to support running two operating systems simultaneously.
FYI, I have had to try supporting Cricut devices for family members for many years. If you purchase a Cricut device, expect extremely poor software and support. I would strongly advise against purchasing a Cricut device due to their poor design & support. Anyone purchasing a Cricut is agreeing to accepting the risk of things breaking with poor support from official channels.
Also, people should not upgrade to any new version of an operating system without verifying all their third party hardware & software are completely compatible. It can take hardware manufacturers and software developers weeks, months, or even sometimes a year before they update their product to support a new OS....sometimes they may never update their product to support a new OS. People who decide to upgrade to a new major version of an OS assume the risk of things possibly breaking or becoming unsupported. It is best to test things out first by running the new version of macOS side by side with the older OS or boot the new OS from an external drive so you can verify all your hardware & software is compatible with the new OS before you make the jump to actually upgrade the main OS boot volume to the new OS (you can then delete the other test OS to free up space).
Sorry if this sounds so negative, but it is so frustrating people keep purchasing a product with such terrible support. There are other options out there which do better with support and which tend to be a bit more open with standards so independent third parties can create alternative software to access the products....Cricut seems to go out of their way to prevent this from happening so people are locked into the Cricut private & proprietary locked down ecosystem.
Check out the Cricut support site for assistance which is hidden at the bottom of the main page instead of a quick & easy to find "Support" option at the top of the page....this is very telling about a company's desire to support a product...they prefer to hide any suggestion that support is necessary, plus they have very basic information on their support site unlike other companies which provide lots of articles for assistance with a product. Even the "Community" link at the top of the page only provides options for promoting the product and not for providing community support for troubleshooting product issues since it could lead to bad press. Maybe I'm wrong about it all.
https://help.cricut.com/hc/en-us