Using a modern gcc with the giga and display shield - query on work done so far

Sorry, I have not tried out new versions of GCC with this board.

As for debuggers. Not sure if any of the below will help or not, but thought I would mention
it as your github issue mentioned your hardware debugger is currently out of commission:

A while ago, I was doing some debugging on the GIGA... Although I think some of the debug support may have changed since I last tried it.

On one thread: I asked @ptillish if he had some suggestions on what one might use other than the Segar...

He mentioned one of these, which I purchased one, which worked...

CMSIS-DAP Compliant SWD Debugger from Alex Taradov on Tindie

But he is not currently selling them, BUT he has github project:
ataradov/free-dap: Free and open implementation of the CMSIS-DAP debugger firmware (github.com)

Which is also setup that it can be flashed on some other boards, like RPI 2040 and PICO... So if you have some of these boards and are in hurry to try something out...

There were a few other threads, where a few us were trying out the debuggers on the GIGA, including:

Not sure if any above will help, but good luck!