A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
Update on the issue. I found someone with an Office 365 license so he can try to open my file with the desktop app. It works without any trouble, no need to repair or launch in safe mode, so we saved a copy of the file without any modification. I could then open this file in Excel for the web once, but when trying to open it a second time it was broken again.
After it autosaves, I noticed my file is down by a few KB though absolutely nothing was modified and I can't open it again. If I restore the previous version, everything is fine again and I can work on it as long as I don't close it.
Also, as a test, I tried opening the working backup and moved one of the sheet. Then I could close and open it without any trouble but as soon as I moved back the sheet to where it was, the file was broken again (it's 100% reproducible).
Even though it seems to be in some very specific cases, as everything was still working fine a few days ago with the exact same file, it clearly tells me a recent update to Excel for the web is the culprit here.