Happening to me in Samsung S22 Ultra- post new software update to Android 13- One UI 5. Its happening in whatsapp, unable to download any media, sending new media is not an issue. But while downloading it shows a range of errors-
media keeps stopping OR
whatsapp can't download because no internal storage is available OR
Unable to download, try later.
I was able to fix my "media storage keeps stopping" messages by going to settings > apps > three dot menu at top right of screen and hitting "reset app preferences". Took care of all of my storage problems. I hope that clears up your problem!