Guter: Allright, this is what happened:
I removed some older saves (0000-0007), 0008 to 0014 remaining. The game started to create saves 0000 to 0004 again, 0004 is the newest, and contains all my progress.
This is somehow problematic, because the savegame properties on the loading screen don't give you any hint what the newest save might be. You have to find the saves in the windows explorer and look for the date.
Furthermore, what happens when the game reaches the range of existing saves when counting upwards the savegame names?
Ah, that makes sense. To name a new save game, it checks if one exists starting at 0000 and counts upwards until it finds that a save does not exist. We had not anticipated players deleting some of the save games.
You can tell which is the latest save by the "Timer" column which records how long the game has been played when the game was saved.
No need to worry about using up all the save slots, it goes up to 99999. If you did have 99999 saves it would save over number 99999 instead.