Edit by @Alaska (Alaska)

T77065#938570
The file output node is working as expected making this report invalid. However, as a design question, what's the possibility of the file output node auto correcting something like //6/a to //6/a/ to avoid the issue described in the original post.

OS: Ubuntu 20.04 LTS
Blender: 2.90 0270941b70d5

• Output images of the compositor always begin with Image, e.g. //6/Image0001.png
• Even if the path does not end with a slash, e.g. //6/hello, the compositor still outputs in //6/hello/Image0001.png

Expected behavior: copying the behavior of the Output properties panel
//6/ -> //6/0001.png not //6/Image0001.png
//6/a -> //6/a0001.png not //6/a/Image0001.png

Broken both with GUI and with terminal rendering