The log says:
:info:build /opt/local/include/spdlog/fmt/fmt.h:31:14: fatal error: 'fmt/core.h' file not found
:info:build # include <fmt/core.h>
:info:build ^~~~~~~~~~~~
The doxygen port doesn't declare a dependency on the spdlog port and we have successful builds of doxygen on all buildbot workers that have tried to build this port (there isn't a Sonoma arm64 buildbot worker yet) so this may be an opportunistic use of spdlog. In fact it looks like doxygen includes a bundled copy of spdlog and is trying to use that but is inadvertently finding your MacPorts copy with which it is evidently not compatible.
If trace mode worked on Sonoma you could use that to hide spdlog during the doxygen build. But since it doesn't, you could deactivate spdlog for the duration of the doxygen build:
sudo port clean doxygen
sudo port -f deactivate spdlog
sudo port upgrade doxygen
sudo port activate spdlog
