I had the exact same issue and was able to fix it. The problem for me was that there are plastic rows along the pins on the connector for the fan. Part of one of these had broken off and gotten stuck into the socket on the TH board, which caused the cable to slip out easily. The piece of plastic was so small that I had to remove it with a needle.
Are you sure it is lined up correctly? In that fist picture it looks like it is not lined up.
I have plugged those connectors in before and had them totally misaligned where it felt like it was plugged in but was off by a whole row of pins.
This is how the connectors should look with all 3 plugged in:
I feel like I’m going crazy because no one else has mentioned this… but it looks like the whole connector has broken off the PCB and is stuck on the plug. If you hold the plug and pull does that part come off?
In your first picture, the 2nd plug is to high on the connector. I can see that the lower row of pins for the second connector (the hot end fan connector). That row should not be visible when the connector is seated correctly.
That is why I pulled the picture from BL’s wiki page, to show you what it should look like.
I don’t think that’s the case. This was mentioned but the cable looks normal to me and their Toolhead PCB board is not missing a connector in the photos.