Press it both ways.
The same chess clock, deployed twice from the same source. One instance was handed to an Interlude node; the other was left on the chain. Pressing the first takes about a millisecond and costs nothing. Pressing the second takes a block and costs gas. Both buttons are below, and every number under them was measured in this tab.
Not configured
This build does not know where the clock is.
It needs two addresses, NEXT_PUBLIC_INTERLUDE_CLOCK and NEXT_PUBLIC_INTERLUDE_CLOCK_DIRECT, and a deployment address is not something a page can guess: it changes every time the contracts are deployed. scripts/clock-demo.sh writes both, with the node and base chain urls, into apps/demo/.env.local.