Since it’s the three-bazillionst time I’m looking this up I’ll write it down here so I can find it easily.
You split an object in two at certain nodes by selecting two nodes and then pressing:
– Shift-B (Break apart at selected nodes) as pointed out on Stackexchange.
– Ctrl-Shift-K (Break apart again but the path/object this time, I guess? This always confuses me to no end, why this is a two-step process? Only the almighty SVG goddess knows)
I’ll preserve the handy graphic that user Brecht (see link above) made in case Stackexchange goes full enshittify mode in the future: