refactor: make [flush] non optional in private API #1575

Job	Run time
build-test-default (ubuntu-latest, ocaml-variants.4.14.2+options,ocaml-option-afl, *.opam !cohttp...	3m 11s
build-test-default (ubuntu-latest, ocaml-variants.5.02.0+options,ocaml-option-afl, *.opam !cohttp...	8m 24s
build-test-default (macos-latest, ocaml-variants.4.14.2+options,ocaml-option-afl, *.opam !cohttp-...	2m 17s
build-test-cohttp-async (ubuntu-latest, ocaml-variants.4.14.2+options,ocaml-option-afl, *.opam !c...	2m 57s
build-test-default (macos-latest, ocaml-variants.5.02.0+options,ocaml-option-afl, *.opam !cohttp-...	5m 7s
build-test-cohttp-async (ubuntu-latest, ocaml-variants.5.02.0+options,ocaml-option-afl, *.opam !c...	8m 32s
build-test-cohttp-async (macos-latest, ocaml-variants.4.14.2+options,ocaml-option-afl, *.opam !co...	1m 51s
build-test-cohttp-async (macos-latest, ocaml-variants.5.02.0+options,ocaml-option-afl, *.opam !co...	6m 59s
build-test-cohttp-bench (ubuntu-latest, 5.x, *.opam )	7m 2s
build-test-cohttp-eio (ubuntu-latest, 5.x, http.opam cohttp.opam cohttp-eio.opam )	4m 5s
build-test-cohttp-eio (macos-latest, 5.x, http.opam cohttp.opam cohttp-eio.opam )	4m 4s
	54m 29s

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