Hi Alice,
We have found the root of our problem.
The P0_6 pin was pulled-down at boot by a 10k resistor. Removing the resistor make the board boot normally (led blinking), soldering it back make the board boot in ISP (led not blinking).
What puzzles us is that the "MCX A156, A155, A154, A146, A145, A144
Reference Manual" and the "UG10151 MCXA14x/15x Hardware Design Guide" clearly states that the ISP pin is P3_29 for LQFP64 and lower pin count (obviously including our MCXA156VLH OP29K), The P0_6 pin act as isp only for higher pin counts.
Page 123 of the reference manual :

Page 9 of the hardware guidelines :

Can you confirm that this behaviour is abnormal?