Why does the phone initially show it's connected (without phone or media signal transmission), then later show it's disconnected, after closing the charging case of the Xiaomi Buds 5?

This occurs because the earbuds and the phone use different Bluetooth connection profiles. A2DP (Advanced Audio Distribution Profile) is utilized for high-quality audio streaming, such as music playback, while HFP (Hands-Free Profile) is used for voice calls. The transition between these profiles can sometimes cause the phone to briefly display a connected status followed by a disconnected status. Despite this display change, the functionality of the earbuds remains unaffected. You can continue using them for audio playback and calls without any issues.