With this extra debug you can see (especially compared to the example on the link) that VIDEO_4_LINUX does not even try to set exposure:
[ +0,000059] video0: VIDIOC_S_FMT: type=vid-cap, width=1920, height=1080, pixelformat=BG10, field=none, bytesperline=3840, sizeimage=4147200, colorspace=8, flags=0x0, ycbcr_enc=0, quantization=0, xfer_func=0
[ +0,000026] video0: VIDIOC_REQBUFS: count=3, type=vid-cap, memory=userptr
[ +0,000050] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000012] OS02C10 6-0036: OS02C10_set_gain called with value 0 which translates to approximately 0.0 gain_multiplication
[ +0,001298] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=4, error_idx=3, id/val=0x9a2003/0x1, id/val=0x9a200b/0xf4240, id/val=0x9a2009/0x0, id/val=0x9a2003/0x0
[ +0,337016] OS02C10 6-0036: OS02C10_set_gain called with value 0 which translates to approximately 0.0 gain_multiplication
[ +0,001736] OS02C10 6-0036: OS02C10_set_exposure called with value 100 us
[ +0,006985] OS02C10 6-0036: OS02C10_set_frame_rate called with value 1000000 which translates to 1.0 fps
[ +0,220208] video0: VIDIOC_STREAMON: type=vid-cap
[ +0,009919] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000093] OS02C10 6-0036: OS02C10_set_gain called with value 13 which translates to approximately 1.6 gain_multiplication
[ +0,001698] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000015] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0xd, id/val=0x9a2003/0x0
[ +0,036059] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000574] OS02C10 6-0036: OS02C10_set_gain called with value 0 which translates to approximately 0.0 gain_multiplication
[ +0,002578] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000020] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x0, id/val=0x9a2003/0x0
[ +0,002500] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000076] OS02C10 6-0036: OS02C10_set_gain called with value 13 which translates to approximately 1.6 gain_multiplication
[ +0,002046] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000022] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0xd, id/val=0x9a2003/0x0
[ +1,795655] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000014] OS02C10 6-0036: OS02C10_set_gain called with value 15 which translates to approximately 2.1 gain_multiplication
[ +0,003559] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0xf, id/val=0x9a2003/0x0
[ +0,238728] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 17 which translates to approximately 2.3 gain_multiplication
[ +0,001435] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x11, id/val=0x9a2003/0x0
[ +0,240842] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 20 which translates to approximately 2.6 gain_multiplication
[ +0,001381] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x14, id/val=0x9a2003/0x0
[ +0,240864] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000014] OS02C10 6-0036: OS02C10_set_gain called with value 23 which translates to approximately 3.2 gain_multiplication
[ +0,001413] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000005] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x17, id/val=0x9a2003/0x0
[ +0,240848] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000014] OS02C10 6-0036: OS02C10_set_gain called with value 26 which translates to approximately 3.5 gain_multiplication
[ +0,001409] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x1a, id/val=0x9a2003/0x0
[ +0,240833] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 30 which translates to approximately 4.2 gain_multiplication
[ +0,001524] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x1e, id/val=0x9a2003/0x0
[ +0,240738] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 35 which translates to approximately 5.0 gain_multiplication
[ +0,001422] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x23, id/val=0x9a2003/0x0
[ +0,240817] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 40 which translates to approximately 5.5 gain_multiplication
[ +0,001647] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000007] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x28, id/val=0x9a2003/0x0
[ +0,240526] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 46 which translates to approximately 6.4 gain_multiplication
[ +0,001362] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000007] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x2e, id/val=0x9a2003/0x0
[ +0,240997] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000014] OS02C10 6-0036: OS02C10_set_gain called with value 53 which translates to approximately 7.4 gain_multiplication
[ +0,001372] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x35, id/val=0x9a2003/0x0
[ +0,240853] OS02C10 6-0036: OS02C10_set_group_hold called - HOLD
[ +0,000013] OS02C10 6-0036: OS02C10_set_gain called with value 57 which translates to approximately 8.1 gain_multiplication
[ +0,001294] OS02C10 6-0036: OS02C10_set_group_hold called - RELEASE
[ +0,000006] video0: VIDIOC_S_EXT_CTRLS: which=0x9a0000, count=3, error_idx=2, id/val=0x9a2003/0x1, id/val=0x9a2009/0x39, id/val=0x9a2003/0x0
You can see id=0x9a200a (exposure) not being set, while 0x9a2009 is being set (gain).
In the example on the link, both values are being set continously.