On opening an EPUB in Sigil, Sigil automatically moves everything into the Text/Styles/Images/Fonts folders.
EPUBs with multiple same-name files in subfolders will open in Calibre's Editor since Calibre doesn't insist on a certain folder scheme.
If you still want to use this EPUB in Sigil, I would recommend renaming the files into something like this:
Part1-Chapter01.html
Part1-Chapter02.html
[...]
Part3-Chapter03.html
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