You do not need to change the bootloader. That wiki page tels you how to load a pre-compiled hex or how to recompile/load the bootloader and sketch. There is an option between those where you only recompile the sketch (not bootloader) and upload that (not a pre-compiled hex). But for that you cannot use the “Uno” board option you need a 3.3v 8Mhz ATmega328p board, there is a bespoke boards.txt entry included on that wiki page as part of the upload new bootloader guide, that could be used, or you could try using a Pro/Pro mini board option as in the edit I just made to my last post.
If you are using the serial port (ftdi header or gpio) to upload your sketches, the install bootloader options will fail as you cannot install a bootloader via serial, only via the 2x6 in-circuit programmer header can you change the bootloader as that is what provides the ability to upload via serial.
[edit - If you have edited the board.txt as part of your previous attempts then you should have a new “8MHz type board” entry you can select when using the Arduino IDE so you may not need to use “pro/pro mini” now]