The following clues(!) are offered:

repot into fresh mix that has some bigger pieces of pumice or vermiculite included because most begonias like to be well-drained. Be sure to take off the roots at the bottom because they may well have rotted. (About a fourth of an inch.) Use either the same size of pot ot one only slightly bigger. Fit the roots, not the top. If there's too much soil around them that hasn't got a spread of roots in, the little root ball could drown or rot.

Unless you have very chilly nights - you could then put them outdoors for a vacation.

Never let them stand in water. The saucer is only to protect your furniture. If they need to drain, put some pebbles into the saucer and stand the pot on them so the water doesn't sit to rot the roots.

Nip off the old flowering stalks. Although it looks like 'flowering forever', they do take a rest and spend some time growing fresh leaves before they start flowering again.

Morning sun and afternoon shade. If it's really hot in your area they're safer behind net curtains. 'Filtered light'.

Let the mix dry out somewhat between waterings, and at least once a month give a liquid feed diluted to the instructions on the label. You could try either orchid food or for african violets, or tomatoes.