It looks like the driver does not get correct response to this:
ret = veyecam2m_read_reg(veyecam2m, VEYECAM2M_MODEL_ID_ADDR, &device_id);
if (ret) {
dev_err(&client->dev, "probe failed \n");
return -ENODEV;
}

I have read about the http://wiki.veye.cc/index.php/RaspberryPI_I2C_confilict_problem ..is this still problem (iam not using DSI display)?. Also this solution recommends to rewire the I2C. At which I2C bus the V4L2 driver actually expects to have the module?

I have also tried to disable the i2c_arm in the startup config, but no help either.

However when I execute the:
astroberry@astroberry:~/raspberrypi/i2c_cmd/bin $ ./camera_i2c_config
setting GPIO for board revsion: c03114
4B(1G/2G/4G/8G)
Set state of 133 to 1
Use i2c-10 for the sensor (-y 10)

Then the i2cdetect finds the device:
astroberry@astroberry:~ $ i2cdetect -y 10
0 1 2 3 4 5 6 7 8 9 a b c d e f
00: -- -- -- -- -- -- -- -- -- -- -- -- --
10: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
20: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
30: -- -- -- -- -- -- -- -- -- -- -- 3b -- -- -- --
40: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
50: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
60: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
70: -- -- -- -- -- -- -- --

However the dmesg still shows:
astroberry@astroberry:~ $ dmesg | grep veye
[ 6.523877] veyecam2m: loading out-of-tree module taints kernel.
[ 6.646795] veyecam2m 10-003b: probe failed
[ 31.835106] veyecam_vana: disabling
[ 31.835117] veyecam_vddl: disabling
[ 31.835125] veyecam_vdig: disabling

Do I need to add the camera_i2c_config somewhere manually that it is executed at every startup before starting of the driver?

I have tested various i2c settings and all seems to reponds as expected so the i2c but definitely works.

On the first day when I got the camera, I was by mistake using the ./cs_mipi_i2c.sh, which is for the CS series, but that was never getting me some proper response. Could it be however that something is misconfigured? I tried for example the ./cs_mipi_i2c.sh -w -f sysreset at that time.

V4l2 mode and Legacy mode are not supported at the same time, see this page for details.
http://wiki.veye.cc/index.php/Raspberry_Pi_Application_Note_Index

Based on your description, I think the mipi data channel is ok.
But i2c can't access to camera correctly. Are you using rpi 4b?
Try

i2cdetect -y 10

See if there is a device with 0x3b address?

OK, I have tested something that worked before to check the camera function and connection:

./veye_raspivid -t 5000 -o ~/tes1t.h264
camera num -1
Hardare version: c03114
mmal: mmal_component_enable w 1920 h 1080 fps 30

raspipreview_create com
mmal: Splitter has 4 output port,you could use num 2,3 for extend

It does not do more at this point, just stops there and no video is recorded. Camera is responding to the I2C commands however.

I have tried to uninstall the V4L2 driver and restart and after that recording works:
I have just executed this one command after the raspberry was restarted (no I2C commands to configure, etc)
./veye_raspivid -t 5000 -o ~/tes1t.h264
camera num -1
Hardare version: c03114
mmal: mmal_component_enable w 1920 h 1080 fps 30

raspipreview_create com
mmal: Splitter has 4 output port,you could use num 2,3 for extend
mmal: running now!!
mmal: running stop!! 0

Video is recorded as expected.

Are there maybe some logs somewhere to see more exactly vhy the V4L2 diver refuses to work? Also when the V4L2 is active, should it prevent the camera to be used othewise, for example to record the video or stream?

Thank you

astroberry@astroberry:~ $ dmesg | grep veye
[ 6.583170] veyecam2m: loading out-of-tree module taints kernel.
[ 6.716455] veyecam2m 10-003b: probe failed
[ 31.844086] veyecam_vana: disabling
[ 31.844103] veyecam_vddl: disabling
[ 31.844116] veyecam_vdig: disabling

What could be still wrong?