The Sin War mod is compatible with D2SE, but due to the lack of a few key files, mod-manager can't identify version and display on lists. Here are two solutions:
(1) Disguise as vanilla patch 1.13d/1.14
It is the easiest way and actually the same as installation instructions in readme file. After copying all files to Diablo 2 directory and overwriting, launch D2SE and click on the upper right button "Start D2" to enter mod.
Characters are not saved separately, and there is no mod information. This solution is too simple to suit a player with numerous mods.
(2) Install customized D2SE mod-plugin
Almost perfect for D2SE users, so to speak. Before dealing with mod-plugin, you must have downloaded mod installation pack in which some files are required in new destination folder, and then follow the steps below:
1. Download and extract mod-plugin file. You will get a subfolder named "The Sin War".
2. Copy "The Sin War" subfolder to "MODS" folder in Diablo 2 directory.
3. Copy Patch_D2.mpq and PlugY.dll to "The Sin War" subfolder. (The original Patch_D2.mpq can be restored from backups if it has been overwritten.)
4. Copy remaining files in installation pack to Diablo 2 directory and overwrite. (Ignore this step if you have done it.)
5. Launch D2SE and The Sin War mod banner appears at the bottom of lists.
Note that D2SE mod-plugin can't work with extra language files. The first solution is the only choice if you have language problems.
The known issue mentioned in readme file is possibly caused by some kind of incompatibility. So far it has not happened to me, and I believe it can be fixed for good by either solution.