everything seems to be very wet
You're right it is very wet at the moment. Get yourself a bamboo kitchen skewer or chopstick or a small diameter dowel rod and insert it into soil. Find a spot where it goes in without contacting a root and plan on leaving it there. Every day remove the skewer and hold it against the underside of your wrist. If it is cool and damp the tree will not need to be watered that day.
Soil with commercially prepared bonsai (sometimes called mallsai) is notorious for being very poor quality and slow to drain, so be careful about watering too often. When you do water, water well, then wait again. Rahter than worry about wiring now concentrate of the soil and your plans, if any, for dormancy.
There have been several recent threads on Chinese Elms:
Both of these owners have similar trees that were allowed to remain in the old, soggy soil for too long. Good quality bonsai soil looks nothing like the muck your tree is currently potted in.
Read over those three threads and get back to us.
EDIT: IT seems that I made an error when linking to the two threads used as examples above. The first thread should not have been cited as an example of poor soil. I was working from memory and neglected to double check that I had the correct threads. My apologies to the OP, other readers and to lms4483.