Make `fdialog_project` up to become the child of `ProjectManager` instead of child of `ProjectDialog` #35094

Job	Run time
📊 Static checks / Code style, file formatting, and docs	31s
🍏 iOS / Template (target=template_release)	1m 49s
🍎 macOS / Editor (target=editor, tests=yes)	4m 3s
🤖 Android / Editor (target=editor)	3m 59s
🍎 macOS / Template (target=template_release)	3m 13s
🐧 Linux / Editor w/ Mono (target=editor)	3m 36s
🤖 Android / Template arm32 (target=template_release, arch=arm32)	3m 28s
🤖 Android / Template arm64 (target=template_release, arch=arm64)	3m 23s
🐧 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)	19m 40s
🌐 Web / Template w/ threads (target=template_release, threads=yes)	6m 39s
🏁 Windows / Editor (target=editor, tests=yes)	11m 1s
🌐 Web / Template w/o threads (target=template_release, threads=no)	7m 12s
🐧 Linux / Editor with clang sanitizers (target=editor, tests=yes, dev_build=yes, use_asan=yes, use_ubsan=yes, use_llvm=yes, linker=lld)	7m 36s
🏁 Windows / Template (target=template_release)	9m 58s
🐧 Linux / Editor with ThreadSanitizer (target=editor, tests=yes, dev_build=yes, use_tsan=yes, use_llvm=yes, linker=lld)	7m 45s
🐧 Linux / Template w/ Mono (target=template_release)	2m 23s
🐧 Linux / Minimal template (target=template_release, everything disabled)	1m 9s
🪲 Godot CPP / Build and test Godot CPP	8m 2s
	1h 45m 27s

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