You want actual tech of the time. That leaves you with clockwork.
When I was a teenager I took apart an old adding machine. It had so many parts!
I use clockwork in the broad sense here - moving parts moved by mechanical energy that output a complex result, like the time or a sum. So too your automatons. They are complicated machines with many parts, powered by a mainspring and clockwork. Big ones might have been retrofitted with steam. In there 1920s there was electricity too but batteries were primitive, so an automaton powered by electricity might need a direct connection like a streetcar; or the electricity could be used to wind the spring.
A machine this complex is not going to dig a ditch or carry a rifle. Humans are cheap and good at stuff like that. But a giant drill might have a mechanical brain to aid it in its job and there might be other roles where, like an adding machine, mechanization offered advantages. I can imagine an ore sorter. You could have a mechanical security system that could have automated weapons.
These things are not going to chat you up like Commander Data. But it is amazing how far machines got with pure clockwork and moving parts.
Shout out to Tik Tok, the clockwork man from Wizard of Oz (the books, not the movie).
Tik-Tok (sometimes spelled Tiktok) is a round-bodied mechanical man
made of copper, that runs on clockwork springs which periodically need
to be wound, like a wind-up toy or mechanical clock. He has separate
windings for thought, action, and speech. Tik-Tok is unable to wind
any of them up himself. When his works run down, he becomes frozen or
mute or, for one memorable moment in The Road to Oz, continues to
speak but utters gibberish.