See my messages in iCloud
How do I see my messages that are synced to the cloud?
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There is no option to view messages at iCloud.com. iCloud messages are viewed on devices. See the following from Keep your messages up to date with iCloud - Apple Support
When you set up iCloud for Messages, your messages are stored in the cloud instead of locally on your device. You can see them on any device that’s set up for iCloud and Messages, including your iPhone, iPad, iPod touch, and Mac.
Because your messages are in the cloud, if you send, receive, or delete a message on one device, those updates appear everywhere. You see the most up-to-date version of your messages, no matter where you access them.