`ResourceLoader`: Fixup management of thread-specific status #34285

Job	Run time
📊 Static checks / Code style, file formatting, and docs	1m 12s
🍏 iOS / Template (target=template_release)	9m 45s
🍎 macOS / Editor (target=editor, tests=yes)	33m 40s
🍎 macOS / Template (target=template_release)	21m 35s
🐧 Linux / Editor w/ Mono (target=editor)	40m 51s
🤖 Android / Editor (target=editor)	24m 30s
🐧 Linux / Editor with doubles and GCC sanitizers (target=editor, tests=yes, dev_build=yes, scu_build=yes, precision=double, use_asan=yes, use_ubsan=yes, linker=gold)	47m 37s
🤖 Android / Template arm32 (target=template_release, arch=arm32)	16m 14s
🐧 Linux / Editor with clang sanitizers (target=editor, tests=yes, dev_build=yes, use_asan=yes, use_ubsan=yes, use_llvm=yes, linker=lld)	36m 10s
🌐 Web / Template w/ threads (target=template_release, threads=yes)	24m 29s
🤖 Android / Template arm64 (target=template_release, arch=arm64)	16m 34s
🐧 Linux / Editor with ThreadSanitizer (target=editor, tests=yes, dev_build=yes, use_tsan=yes, use_llvm=yes, linker=lld)	30m 54s
🌐 Web / Template w/o threads (target=template_release, threads=no)	24m 17s
🐧 Linux / Template w/ Mono (target=template_release)	25m 59s
🏁 Windows / Editor (target=editor, tests=yes)	53m 57s
🐧 Linux / Minimal template (target=template_release, everything disabled)	15m 18s
🏁 Windows / Template (target=template_release)	34m 48s
🪲 Godot CPP / Build and test Godot CPP	7m 47s
	7h 45m 37s

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