Need to change external hard drive format without losing files??

Hello all, I have a 2016 Macbook Pro laptop that is running Catalina 10.15.6, and I have a 2TB external hard drive that I use to save folders and files, but I am having an indexing issue with my laptop in that it will not search the external drive once it is connected to the USB port....

I can open the external drive just fine, and can read & write to it, but it will not let me search for specific files / folders using Finder, and this is apparently an indexing problem, or so i have been told. I have been in touch with Apple Support concerning this, but was finally told that the format of the external drive (ExFat) minimizes the support they can offer. As such, I would like to change the format of the external drive, but not lose everything that is saved on it.

This is not a tragedy really, but it would be nice to know how nonetheless, and I would appreciate any advice here.

Oh yes, and Thanks in advance!!