This is the error/message that is displayed in the plex web interface while the docker logs are continuously looping the drive full error every few seconds that others are reporting.
I too had this problem, and noticed I also had my trans_dir set to /dev/shm. After changing that to the default value of "/config/transcode" (to at least test it), the 1.40.3 versions now work, and plex starts properly. I am betting that in version 1.40.3 plex added a space check or something for the transcoding directory with some new minimum that is greater than 64MB.
Adding the proper config binhex mentioned earlier in this thread (pointing trans_dir to /transcode, and adding a /transcode mapping to /dev/shm), plex now works properly again using the 1.40.3 versions.