It’s not exactly with the UI you suggested, but you can use PlutoUI.Clock() for this; for example
which is from my work-in-progress notebook https://github.com/ericphanson/UnbalancedOptimalTransport.jl/blob/305544b877b0fba57bc24329b814c6d216de47e1/scripts/visualize_pluto.jl
You just use t as your timer, which just counts up when you press play, and resets to 1 if you stop and start it. You can use mod1(t,N) to loop after N steps, etc.