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I got this bonsai in late June and I've been taking good care of it ever since, however I've noticed that the tree has not grown out any new branches or leaves for a couple weeks now.

There was a lot of growth in early July but the tree has entered a stage where it lost a few of its leaves and ever since has stopped growing new leaves completely. I have looked closely at the leaves and I can see new buds however i haven't seen them grow at all.

I have read that this is an elm so I have left it outside in the shade where the sun is not as harsh and im keeping up with watering it as well. I am new to the topic of bonsai so please tell me if I'm doing anything wrong that could negatively impact the tree and could anyone tell me if the bonsai appears to be healthy in general.
(Pictures attached below.)

Put it outside in the sun and water it when it is dry. A little fertilizer would help.

Trees grow a lot of leaves and elms make new branches for a while but when summer sets in they stop,the rapid growth and soak up sun, getting ready for winter.

You can find out about winter care in your area from a local bonsai group.