Those beige, mustard-seed-sized spheres and white cottony webbing at the base of your hosta? Textbook Southern blight (crown rot), caused by the fungus Sclerotium rolfsii. The "beads" are sclerotia—survival structures that persist in soil for years.
Strangely, you water sparingly. So how did a moisture-loving fungus take hold? The answer came in your follow-up: you used a strong, direct stream of water when hand-watering. That force bruised the tender petioles, creating entry points for the pathogen. A gentle shower setting would have prevented it.
Remove and destroy the infected plant—don't compost it. Solarize the soil or replace it in that spot. Avoid wounding stems when watering. The good news: your other 12 divisions from the same parent plant are unaffected, and the disease doesn't spread rapidly without mechanical injury.

Hosta stem rot with sclerotia

Cottony mycelium at crown
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