Do you mind checking beginning of file blockchain_headers with hex editor/viewer? I tried on my device, but mostly it only contain zeroes. I suspect Electrum only request needed block header rather than all block header.
Yes, although I simply read the file as a byte stream not with hex editor, the file starts with the genesis block's header ie. 0x01 followed by 35 zeros (previous hash) then 0x3b (merkle root) and so on.
I've had my Electrum for a very long time though. The file was created in 2019! Maybe they changed some stuff like after the introduction of checkpoint header.