I don't re-pot very often, but if I do, it's because the roots have taken over the pot and there is more roots than soil, or, water will run straight threw without wetting the roots properly or, the
plant is no longer
growing.
If something needs to re-potted, I like to tackle that in the
spring, unless it's severally root-bound and needs re-potting right away to be healthy.
Otherwise, I would leave it be. Most
plants like to be on the pot-bound side anyway.
As long as the soil in the begonia has good drainage and your seeing that the plan is starting to improve, I would also leave that one alone.
Sometimes those
plant places put
plants pots that are too big, then I would downsize so the root-ball has just an inch between the root-ball and inside of the pot.Same thing if you go up a pot size.
Perlite added to soil can help with drainage.
