External HDD EXFAT partition not mounting on MacBook

You can try mounting the exFAT volume as read-only which may possibly allow you to access the volume. With the drive connected, use Disk Utility to identify the device identifier for the exFAT volume which will be in the form of "diskXsY" where "X" & "Y" will be numbers such as "disk3s2".

Once you have that device identifier (it may change every time you reconnect the drive), use the following command in the Terminal app making sure to replace "diskXsY" with the correct device identifier for the exFAT volume:

diskutil  mount  readOnly  diskXsY

If the exFAT volume has the device identifier of "disk3s2", then the command would be:

diskutil  mount  readOnly  disk3s2

If the volume mounted successfully, then you should be able to use the Finder to access it at "/Volumes/<exFAT-volume-name>".

If this does not work, then you should look into a data recovery app to attempt to access the data on that volume. Stellar Data Recovery and Disk Drill tend to be popular options. They should provide you with a demo mode so that you see what files it locates, but you will need to pay in order to retrieve any actual data although the app may offer to recover a few small files for free in the demo mode.

In the future, make sure you have frequent and regular backups of your computer and all external media (including the cloud) which contains important & unique data.

Edit: I forgot to include links to those data recovery apps mentioned:

https://www.stellarinfo.com/

https://www.cleverfiles.com/data-recovery-software.html

Try using Disk Utility to Repair/FirstAid the ExFAT portion of the physical drive.

(A drive does NOT need to be Mounted to be repaired. In fact, the first step for Repair is to Un-Mount if already Mounted.)

Then after you run the Repair, either the drive will be fixed up enough to be Mount-able, or it will be in the same sad state it is in now.

Disk Utility Repair won't make it any more broken than it already is.

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...and if you manage to dodge this 'near-death experience', how are you going to make sure all these files are backed up in the future? Need suggestions?

the most common reason a Volume can not be Mounted is because its Directory is inconsistent (aka "damaged").

Repair does uses the slight redundancy built into the directory data structures to repair detected damage in the directory. No data blocks are even referenced. This is intended to make the drive Mountable and its files quickly accessible.

What device Wrote these files initially?