Refactored multipart put head request #2299

Job	Run time
macos12	19m 31s
MemoryTest (glibc_debug)	11m 23s
clang-tidy	4m 1s
MemoryTest (sanitize_address)	13m 12s
Linux (ubuntu:24.10)	12m 44s
MemoryTest (sanitize_others)	11m 25s
Linux (ubuntu:24.04)	11m 57s
MemoryTest (sanitize_thread)	5m 3s
Linux (ubuntu:22.04)	12m 49s
MemoryTest (thread_safety)	11m 13s
Linux (ubuntu:20.04)	11m 34s
MemoryTest (valgrind)	23m 23s
Linux (debian:bookworm)	12m 2s
Linux (debian:bullseye)	11m 45s
Linux (rockylinux:9)	12m 27s
Linux (rockylinux:8)	12m 55s
Linux (fedora:41)	11m 41s
Linux (fedora:40)	11m 35s
Linux (opensuse/leap:15)	12m 10s
Linux (alpine:3.20)	11m 55s
	4h 4m 45s

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