The solution was to use .enable instead:
programs._1password.enable = true;
programs._1password-gui.enable = true;
When enabling /run/wrappers/bin/1Password-BrowserSupport gets exposed: https://github.com/NixOS/nixpkgs/blob/1c851e8c92b76a00ce84167984a7ec7ba2b1f29c/nixos/modules/programs/_1password-gui.nix#L46-L53