Perfectly running Arduino Uno Rev3 Not accepting new codeAvrdude

This shows the bootloader is already present on the ATmega328P microcontroller on the Uno. So I don't think there is any hope that doing a "Burn Bootloader" operation could help your problem.

I'm not sure.

In theory, even though the "Arduino as ISP" programmer can only be used to program targets that are a microcontroller of the AVR architecture, boards with a microcontroller of any architecture should be usable as the programmer board. My experiments have shown that some boards unfortunately can't be used as "Arduino as ISP" programmers.

I just made a quick test of using an ESP32 board as an "Arduino as ISP" programmer and the "Burn Bootloader" process failed. But I didn't put a lot of effort into troubleshooting the problem so it is possible it was a user error rather than a fundamental incompatibility of the ESP32 board in this application.