Auto merge of #56961 - pietroalbini:gpg-beta, r=pietroalbini

[beta] Backport fixes to build-manifest

Backports the following changes to beta:

* #56703: Fix build of the `build-manifest` tool *(partial, just added last commit)*
* #56783: Add `--pinentry-mode=loopback` to deployment script
* #56735: Fix gpg signing in manifest builder

r? @ghost
cc @Mark-Simulacrum @alexcrichton