What version of the app are you using? There were some issues with heic photos a while ago, so making sure you have the most current version may help.
Are you taking photos with the phone’s default camera app, or another app? I’ll see this happen if I try to import a photo taken with Seek, for example.
I am having the same problem. A week or so ago after the iPhone update, iNat stopped picking up the date/time from pictures uploaded on the mobile app. Same issue even with pictures that were previously uploaded with no issues before.
Can you post the app version and device that you are using?