These are so much more fun when they stay alive. Yours are so lovely, hope you find your groove with them. I killed a BUNCH in the learning process. When you do find what works for you, in your house & style of care, you *will* have an army of beautiful Begs, good vibes! I'll share what works for me - now, finally.
These are so easy to rot during winter, I let them get very dry. I've also found they do very well as companions to other plants that are more thirsty and have deeper roots. The other plant(s) populate the lower part of the pot with roots, helping to ensure the Begonia roots & rhizome are never soggy.
"I read they like more shallow tighter pots."
This kind of advice isn't about the size of the pot, it's about avoiding rotting the roots by having a smaller volume of soil that can dry more quickly.
"So I transplanted them into only slightly bigger pots. I did not have good potting soil for them so I mixed some topsoil that is sandy with a bag of cactus mix I had. Certainly heavier soil than they were in."
This concerns me a lot. The top soil and sand are tiny particles that fit very closely together, with no air between them. Roots need oxygen & moisture at the same time to function. Only moisture = rotting. Only air = drying & dying.
In a pot, the more chunky/porous/airy the soil, the less likely it is to cause roots to rot. One can compensate by having less soil/smaller pot, using an unglazed clay pot that can breathe around the sides, adding a lot of perlite, and/or eliminating the tiny particles (of anything, such as clay, sand, peat, actual "dirt,") as an ingredient. Starting with something called cactus mix instead of potting soil is usually pretty easy to do, and should, in theory, have a much smaller percentage of tiny particles. From there, you may or may not want to add more perlite, or feel like it is ready to use as-is. Not all bags/brands will have the same stuff, so impossible to say what to do in general. But remember, drying often is great, if you enjoying watering plants.
When the days are shorter, temps are cooler, most plants use a LOT less moisture, Rex Begonias included. (And the sun rays are much weaker, so plants that wouldn't appreciate direct sun during summer may enjoy some during winter.) The thick, fleshy rhizomes of these Begonias store moisture. If they happen to get too dry, leaves that look perfectly fine will suddenly fall off. Not desirable, but much better than death via rotting. Not recommending letting your plants dry to that point, but wanted to share that benchmark for reference & confidence. Once they get a drink, new leaves will pop out.
With plants that can rot so easily, and if you are the type who wouldn't mind doing such a thing, you may do better watering with a squirt bottle, set on a spray/mist pattern (not 1 stream of water.) This allows you to add some moisture without getting soil completely soggy. Except for a few really thirsty guys and gals, this is how I water most of my plants during winter. Adding water this way also prevents the movement & compacting of soil particles that can happen when using a single stream or flow of water, like one gets from a watering can, faucet, or cup. Getting the leaves wet can facilitate surface pathogens that love Begonias so much, so I do try (and recommend) to avoid that. Wet leaves do not = humidity.
During summer, I put these outside in bright shade, and/or morning sun, and keep much more moist, not getting very dry at all.
HTH!
The third photo is the one on my back porch that showed back up after I'd put a cutting of an Aralia in the soil.
