I managed to solve it by downloading the .bin file first to SPIFFS and then, at the next reset, doing the firmware update. After removing the .bin file.
I decided to do so after I read dozens and dozens of contents on the internet, all talking about problems with the ESP8266httpUpdate.h library update
And I've already disassembled everything here, because from now on I'm going to use only the ESP32 in my tests and learning.
That's why I changed the post. I will no longer be able to do tests with the ESP8266.
Good week.
NOTE: By the way, I don't understand why this forum keeps old posts accessible by just clicking on the pencil there (icon that shows that the content has been edited). People have access to what you (in my case) wanted to delete. It's strange because several times I forgot and posted content with my credentials, passwords, etc. and moments later I noticed the forgetfulness and edited it by deleting the inappropriate content. But now I realize that this is useless because just click there on the pencil.
Anyway, there must be a reason that I still don't understand.