The Messages App is splitting my RCS groupchats across my iPhone, iPad, & Macbook Air devices.

After my iPhone 15 Pro updated to iOS 18, I began creating RCS group chats for the circle of family and friends that had mixed iOS and Android smartphones. The RCS functionality was a bit buggy but overall was stable. Last month, I updated my 7th Gen iPad to iPadOS 18 and that is when most of my RCS groupchats began to randomly split into multiple threads within the Messages app. I couldn't figure out a fix so I decided to disable the iCloud functionality on my iPad Messages app. Now I recently purchased the M3 Macbook Air with MacOS 15 (Sequoia), and the issue has again manifested itself. My RCS groupchats split into random new threads that also appear on the other iOS users of the RCS groupchats. Any idea what is going on? The issue only goes away when I disable iCloud on my Macbook's Messages App.