No, there is no automatic increase in residency spots when a new med school opens.
But there is currently an excess of first year residency positions. In the 2022 Match, 36,277 first year residency positions were available. There were 28,337 US medical grads (MD and DO combined) in 2021. (Number of grads for 2022 not yet available.)
The excess positions are filled by US IMGs (US citizens who studied medicine abroad) and FMGs (Non citizens who graduated from foreign medical schools)