They do! Anna has been building up her flight status on United since her Sprinklr days, so she is likely a Million Miler by now. This comes with early boarding and first class upgrades when you book with them.
She used to only fly first class, up until maybe 2019. Two things happened: Anna got bigger, and United switched their first class seat configuration on all but their regional flights. Instead of two larger seats side by side, they created private pods that can be set to either as easy chair configuration, or a full bed. The pods have a console between them with an opaque plastic divider that can be raised to make a private "room".
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As you can see, there is no way Anna can squeeze herself into a pod, even the largest version. She has indeed eaten herself into steerage, where she needs three seats to fit.