Will the music resume automatically if either earbud of the Redmi Buds 6 is removed and put back on?

With the wearing detection feature enabled, when you remove the earbuds while music is playing, it will automatically pause. If you reinsert the earbuds within 2 minutes, the music will automatically resume (regardless of whether the removed earbud is placed back in the case). For video playback, whether the video automatically resumes upon reinserting an earbud depends on the video APP. Some video APPs cannot resume automatically.
Note:
If the music continues playing when the earbuds are in the charging case, it is due to the charging case powering off from a low battery. If the charging case is powered off, the earbuds and the phone cannot communicate, so the earbuds will assume they are not in the case and maintain a connection with the phone, continuing music playback.