Are you deleting the ships uring a game session or from the main menu?

Do you have steam cloud enabled?

I actually tried all that stuff. I disabled steam cloud for GC4. It worked at first, but then a couple days later they came back anyway. I deleted the ship designs in the program folder, again I noticed the designs came back. I delete many of the designs everytime I play just to get them out of the way temporarily, they always come back.

FYI - I have Steam Cloud saves for GC4 explicitly turned off.

That is entirely possible.

This is relatively new system and I am not accustomed to "My Games" folder being hosted on OneDrive.

I think there is a problem with the way the game communicates with Steam to remove a civ. Steam stores zip files of everything downloaded from its workshop in a local directory. Since I have GalCiv4 installed on drive D, the location is D:\SteamLibrary\steamapps\workshop\content\1357210 on my computer. It contains a separate folder for each item, which contains a zip file with all the content for that item. I think that Steam will use this as a way to restore something it thinks is “missing”.

In the past I downloaded a civ named “Eye Crunchies” from the Steam Workshop. After it appeared in a game, I realized it didn’t have a “Civilization Name”, but only a “Civilization Short Name”, so I used GalCiv4’s “Choose Civilization to Lead” screen to delete it. I had read about the problems deleting civs, so I also went into the Factions directory and made sure there weren’t any files still there.

This weekend, a civ that I had made appeared as a random civ in a game. I decided I didn’t like it, so I went back to the “Choose Civilization to Lead” screen to delete it. While there, I noticed the “Eye Crunchies” civ was back.

I am aware of the continuing problems with “deleted” civs still hanging around, so I also deleted the “Eye Crunchies” civ and checked to see if it came back. I was doing other things with the game which included starting and stopping it several times. I didn’t notice how long it took, but the “Eye Crunchies” civ did come back.

I deleted it more than once, and it came back every time. I tried all the variations to get rid of it, but it always came back.

Finally, with GalCiv4 not running, I went into the Steam workshop and unsubscribed from it there. The “Eye Crunchies civ has been gone since then.

I'm not sure if I've had trouble getting rid of civs I've downloaded from Epic/Stardock.

I have had Steam Cloud disabled in global Steam settings for several years because I don't use it. It is also off for each individual game, including GalCiv4. I don't use any cloud-based substitute, like One Drive, instead of local disk storage.