I have the same problem which started last week, about 7/22/2020, up until then I was able to send photos and attachments, then after a Catalina crash/restart overnight or an auto update to the system, iMessage would not send attachments when drag and dropped to the iMessage window. Tried copy and paste and that doesn't work either.
I have a 2019 iMac 27" with Catalina MacOS 15.5.6. These are files from an external HD, NOT a NAS drive, which have always worked up until last week. Just hangs at the end of the iMessage send progress bar and then gives error alert that message was not sent. I have restarted which did not fix it. I created a new user and logged in as new user which did not fix it either. SO it is a Catalina 15.5.6 update issue. I got a notice from Drive Genius that system files had been changed from the last log in. One of the was a new apple.com iMessage file: com.apple.installer.osmessagetracing.plist
Tried the suggested workaround of dragging the file to the desktop first and then to the iMessage text box and that worked. So iMessage can't access external HDs apparently. This is unacceptable.