I think bandwidthPartInactivityTimer is used in BandwidthPart-Config & its is used when the network releases the timer configuration, the UE stops the timer without swithching to the default. Sequence is like:
The UE starts the timer when it switches its active downlink BWP to a downlink BWP other than the default downlink BWP.
The UE restarts the timer to the initial value when it successfully decodes a DCI to schedule PDSCH(s) in its active downlink BWP.
When the timer expires, the UE switches its active downlink BWP to the default downlink .
Reference- 3GPP TS 38.331,sec6.3.2