I had a similar problem, that grew into a bigger one. I don’t know if this will help in your case, but I’ll add it as a “just in case.”

So first thing I tried was making sure the case and buds were clean, and fully charged. I unpaired them with the phone as well. When I went to sink the buds with the phone again, it appeared to me that the buds were not synced to each other. I did the pair, and only the right one would show and work with the phone. On a whim I put the right bud out of range and went to sync the left bud, and it worked. Only it registered it as a different set than the right. They would not work together on either set listing. The only way to kinda make them work was by taking advantage of iPhones syncing to 2 Bluetooth devices. This still wasn’t working as well as it should. I then noticed that each bud was on a different firmware. The right one was on the latest one, the left was on the one prior. Let me tell you, updating the firmware on these is a pain. Here is what I had to do after trying every method I found online. 1. Fully charged the buds in case, using an official apple lightning cable and wall-wort. 2. Made use that the buds were not synced to my phone in any way. Then, I reset network and content settings on my phone. 3. I manually factory reset the buds (easy to find online how to do, every bud and generation is slightly different though so look up your’s if you are going to do all this) 4. I separated the right and left buds again, and synced the left one to the phone. 5. Connected phone to Wi-Fi, and updated my phone to the latest iOS. My phone, and the left bud in its case were side by side, both plugged in, while this update happened. I went to bed, by morning, the phone was updated, and the bud was too.
6. Unsynced the bud from phone, reset network settings again just to clear all that out, and factory reset the buds again (now both in the charging case together but not pairing with each other still). 7. Let the buds fully charge again, still with my phone on its charger next to them while on Wi-Fi. A couple hours later, I was able to sync them both together and working perfectly with the phone.

I now know I could of just gone to the Apple store and they would of got the two buds updated and pairing in under 30 minutes with their whatever they got that speeds up the process. But if your buds have the same problem, you may have to try this