To solve the SD card showing up in Device Manager but not showing up in Disk Management issue, you can try a new SD card reader, update the card reader driver, reinstall the SD card driver, or go to a local disk repair store. Check the methods below for more detailed fixes for your situation.
If you are using an SD card reader:
Fix 1: Change a new card reader. Your Windows operating system does detect an external drive, and that's why your SD card is showing up in the Device Manager. However, due to the faulty or outdated SD card reader not working, the system fails to read your memory card and therefore makes it inaccessible in Disk Management. In this case, trying out a new SD card reader can fix your issue.
Fix 2: Update an outdated SD card driver. If the driver of your SD card reader is outdated and causes your SD card not recognizing, click on Device Manager > SD card, and right-click on it to choose Properties > Driver. You can find the Update driver option in Device Manager.
Fix 3: Reinstall the card driver. If the driver is not properly installed or it's still not working after updating, the last try is to reinstall it. Hopefully, your PC can read your memory card after solving the driver issue.
If you are not using an SD card reader:
Since you didn't mention the SD card reader, chances are that you insert the memory card directly into your PC. In this case, it's possible the SD card itself is physically damaged and loses the connection with your PC. In terms of the physical damage, you are suggested to find a local disk repair store for help.