The TLE9879 is tested according to LV124 test standard.

Is there incorrect LIN communication mode when VS (voltage slope) rise times are slow during TLE9879 power-up sequence test?

In the car, we expect every possible voltage slope and transition. Even slower slopes should not have an influence on the functionality.
When voltage slope transitions are slow during power up sequence test, if the transceiver is in LIN Normal Mode (LNM) instead of LIN Receive Only Mode (LROM), VS undervoltage can be triggered, which causes the LIN to go in Receive-only mode.

LNM to LROM transition is also executed when:
• MODE is configured to LIN Receive-Only Mode or
• Feedback signals of Mode and Slope Mode are not ok or
• VS undervoltage flag (VS_UV_STS) is set or
• LIN transceiver OT_STS or OC_STS are set or
• TXD_TMOUT is set

LROM to LNM transition is executed when:
• MODE is configured to LIN Normal Mode and
• Feedback signals of Mode and Slope Mode are ok and
• VS undervoltage flag (VS_UV_STS) is not set and
• LIN transceiver OT_STS and OC_STS are not set and
• no TXD_TMOUT is set

For further information, please refer to the TLE987xQX User Manual (Page 651) under User Manual in the below link.
https://www.infineon.com/cms/en/product/microcontroller/embedded-power-ics-system-on-chip-/3-phase-bridge-driver-integrated-arm-cortex-m3/#!documents