Can you split washer/dryer and share with standard 3 prong
I would say NO based on the info provided. a 30 amp circuit will first normally be 240v.  But even if it is something I have not seen the Dyson will only be rated for a 20 amp circuit so making a splitter would create multiple code violations if regulated by the NEC.
If it is a 20 amp 120v people all splitters all the time I do not allow them at my work if they need additional outlets I put in new circuits. However there are UL listed splitters so in that if used they would be “safe”.
the code for the laundry circuit is that it has no other outlets so it would be a minor issue and you would only need to worry if the code police show up. (Code police not real a joke)