[Web] Refactor Editor web server. #21898

Job	Run time
📊 Static checks / Code style, file formatting, and docs	44s
🍏 iOS / Template (target=template_release)	3m 50s
🍎 macOS / Editor (target=editor, tests=yes)	4m 28s
🍎 macOS / Template (target=template_release)	3m 20s
🤖 Android / Template (target=template_release)	4m 43s
🏁 Windows / Editor (target=editor, tests=yes)	9m 17s
🏁 Windows / Template (target=template_release)	6m 59s
🌐 Web / Template w/ threads (target=template_release, threads=yes)	4m 5s
🌐 Web / Template w/o threads (target=template_release, threads=no)	4m 4s
🐧 Linux / Editor w/ Mono (target=editor)	3m 20s
🐧 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)	11m 37s
🐧 Linux / Editor with clang sanitizers (target=editor, tests=yes, dev_build=yes, use_asan=yes, use_ubsan=yes, use_llvm=yes, linker=lld)	5m 41s
🐧 Linux / Editor with ThreadSanitizer (target=editor, tests=yes, dev_build=yes, use_tsan=yes, use_llvm=yes, linker=lld)	6m 17s
🐧 Linux / Template w/ Mono (target=template_release)	1m 6s
🐧 Linux / Minimal template (target=template_release, everything disabled)	48s
🪲 Godot CPP / Build and test Godot CPP	6m 51s
	1h 17m 10s

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