I don’t want Live as midi master, in my setup it’s only used as an end-of-chain pedal.
I think I figured out why tempo is jumping on start: ST seems to reset midi clock and retrigger when you press either start or stop button, making the tempo jump for a few seconds.
Seems weird that Live doesn’t reset midi clock when receiving start/stop commands, but as it’s only a few seconds I can live with it, and use wired midi directly from ST to sync my other devices.
For completeness I tried all modes indicated in this post: Ableton as clock slave drift - SOLUTION - #4 by Schnork but the default one seems to work the best. “bad” midi clock made the clock less jumpy but also less reactive on tempo changes.