On a 2019 16" MBP, running 10.15.2 (19C57), I'm having similar issues.
a) I removed a 2 TB SSD I got from Crucial/Micron a few years ago (MX300) from a 2012 MBP. I installed the drive into a Cable Matters enclosure with a USB 3.1 Gen 2 interface. The drive has about 1 TB of data on it.
b) I'm using a USB-C to USB-C cable to connect it to the 16" MBP.
c) Leaving the 16" computer connected to power and set to not go to sleep (except the display), I let Spotlight run overnight, so it could index the external drive on the new computer. It seems to have worked fine.
d) Today, I've been copying large numbers of files from the external SSD to the internal SSD of the new computer. Finder searches seem to work OK. Copying and pasting went fine for awhile. When I got to working with images, though, the drive (or connection, or something) started making the Finder unresponsive.
e) I have about 50,000 images on the external drive. I was hoping to be able to exclude the Pictures folder on the external drive when searching for images (since iCloud had already copied my Apple photos to the new computer), but I'm not sure that the Finder allows one to exclude a particular folder from a search. Anyway, I narrowed the list of interesting images by only searching for image files greater than 900 KB in file size. That got me down to about 5000 images.
f) At first I tried selecting all those files and copying them to the clipboard. This resulted in the Finder becoming unresponsive and eventually the external drive was ejected (by some process, not by me). I wondered if maybe I had selected so many images that I ran out of of RAM in the copy process. I rebooted and started over.
g) This time I copied about 500 files (~ 7 GB) to the clipboard and then to the internal drive. That went fine. Then I selected the next ~ 700 files (~ 31 GB) and copied them to the clipboard. That group also copied to the internal drive. When I selected the next group, the Finder again became unresponsive and I had to relaunch it. It took what seemed to me like a long time to relaunch (~ 30 seconds or more). Over the next few tries, I had to relaunch the Finder multiple times. Sometimes the external drive would remount and sometimes it wouldn't. (Even if Disk Utility could "see" the external drive, it might not mount it.)
h) Now, I seem to be able to replicate this problem (that is, make the Finder unresponsive) just by browsing certain files on the external drive. For instance, some of the images on the external drive are named "CCAPxxx.tif" and/or "CCAPxxx.png". If I skip past these files in the Finder search results window, the Finder continues to work. However, if those files are visible in the Finder search results window (or maybe if one of them is selected), the Finder becomes unresponsive and needs to be relaunched, and the external drive will likely be disconnected in the process.
Thanks for reading.