Hmm.. if you have tested a different port and cable, then the problem may be a by-product of the exFAT format.
If you are using the drive to share files between a Mac and PC, then using the exFAT format is a must.
If you are using the external drive strictly for Mac file storage and backup, then Mac OS Extended (Journaled) or APFS is the preferred format to use. see > https://www.hellotech.com/guide/for/how-to-format-a-hard-drive-for-mac
Problem you have now is, that re-formatting an external drive erase's all of the current data on it and you will need to copy the current data to another drive, then copy that data back after reformatting the external drive.