iPhone 13 Bluetooth audio not working after iOS update
Update to ios 16.3
Update to ios 16.3
Bluetooth audio issues on an iPhone can stem from several different causes. Some of the most common include:
Hi, your iPhone 13 should be upgraded to the latest version, currently iOS 26.5. The upgrade will likely resolve any Bluetooth issues.
Update iOS on iPhone - Apple Support
Based on the title of the post: "After iOS update"
Not every issue an individual encounters on their device can be attributed to an iOS update. If the update itself were the root cause, then every device running that same version of iOS would exhibit the identical problem. In such a scenario, the forums would be flooded with countless posts reporting the same malfunction, creating an unmistakable wave of complaints that no one could possibly overlook. The absence of such widespread reports strongly indicates that the issue is not systemic, but rather specific to the device in question.
You may get better and prompt responses if you may kindly provide the iPhone Model that you have and the iOS version if it is known to you and re-post.

With the limited information that you have provided, It is hard to even guess the problems faced by you.
You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.
iPhone 13 Bluetooth audio not working after iOS update