How to disable camera shutter sound without rooting the phone?

I have a Google Pixel 6a (bluejay) phone. On this phone camera makes shutter sound when I take a photo. I have looked up the phone by IMEI by going to https://store.google.com/us/device-authenticity?id=[IMEI] URL and it shows "Intended region: IN,JP". I have previously installed LineageOS and rooted it to remove the files /product/media/audio/ui/camera_click.ogg /product/media/audio/ui/camera_focus.ogg, /product/media/audio/ui/VideoStop.ogg and /product/media/audio/ui/VideoRecord.ogg. This removed the sound, but because of the root banking applications complained, so I reinstalled the system to CalyxOS without wiping. Now I want to remove the same .ogg files without rooting the phone. I have downloaded https://release.calyxinstitute.org/bluejay-factory-25608200.zip file linked from the page https://calyxos.org/install/devices/bluejay/linux/ . It is an archive with all partition images. Inside an archive there is another archive bluejay-bp1a.250505.005/image-bluejay-bp1a.250505.005.zip which I unpacked. This archive in turn contains product.img file. I unpacked product.img by running unzip image-bluejay-bp1a.250505.005.zip product.img. I confirmed that product.img contains the files media/audio/ui/camera_click.ogg and similar. I tried to mount the image and got this error:

# mount -o loop product.img /mnt/
mount: /mnt: wrong fs type, bad option, bad superblock on /dev/loop0, missing codepage or helper program, or other error.
       dmesg(1) may have more information after failed mount system call.
# dmesg | tail -1
[360861.911279] EXT4-fs (loop0): couldn't mount RDWR because of unsupported optional features (4000)

I ran e2fsck -E unshare_blocks product.img and then tried to mount again: Then the image mounted successfully with mount -o loop product.img /mnt/. I then modified the image:

cd /mnt/media/audio/ui
mv camera_click.ogg camera_click.bak.ogg
mv camera_focus.ogg camera_focus.bak.ogg
mv VideoStop.ogg VideoStop.bak.ogg
mv VideoRecord.ogg VideoRecord.bak.ogg
cd /
umount /mnt

Then I rebooted the phone to fastboot with adb reboot fastboot and flashed the modified product.img to both slots:

# fastboot flash --slot=all product product.img
Resizing 'product_a'                               OKAY [  0.019s]
Sending sparse 'product_a' 1/7 (262112 KB)         OKAY [  6.272s]
Writing 'product_a'                                OKAY [  1.279s]
Sending sparse 'product_a' 2/7 (262128 KB)         OKAY [  6.243s]
Writing 'product_a'                                OKAY [  1.227s]
Sending sparse 'product_a' 3/7 (262120 KB)         OKAY [  5.996s]
Writing 'product_a'                                OKAY [  1.313s]
Sending sparse 'product_a' 4/7 (262120 KB)         OKAY [  5.941s]
Writing 'product_a'                                OKAY [  1.199s]
Sending sparse 'product_a' 5/7 (262124 KB)         OKAY [  5.985s]
Writing 'product_a'                                OKAY [  1.262s]
Sending sparse 'product_a' 6/7 (262104 KB)         OKAY [  5.968s]
Writing 'product_a'                                OKAY [  1.318s]
Sending sparse 'product_a' 7/7 (161293 KB)         OKAY [  3.752s]
Writing 'product_a'                                OKAY [  0.967s]
Resizing 'product_b'                               OKAY [  0.014s]
Sending sparse 'product_b' 1/7 (262112 KB)         OKAY [  5.982s]
Writing 'product_b'                                OKAY [  1.258s]
Sending sparse 'product_b' 2/7 (262128 KB)         OKAY [  5.930s]
Writing 'product_b'                                OKAY [  1.256s]
Sending sparse 'product_b' 3/7 (262120 KB)         OKAY [  5.992s]
Writing 'product_b'                                OKAY [  1.274s]
Sending sparse 'product_b' 4/7 (262120 KB)         OKAY [  5.932s]
Writing 'product_b'                                OKAY [  1.247s]
Sending sparse 'product_b' 5/7 (262124 KB)         OKAY [  6.002s]
Writing 'product_b'                                OKAY [  1.252s]
Sending sparse 'product_b' 6/7 (262104 KB)         OKAY [  6.221s]
Writing 'product_b'                                OKAY [  1.293s]
Sending sparse 'product_b' 7/7 (161293 KB)         OKAY [  4.136s]
Writing 'product_b'                                OKAY [  0.917s]
Finished. Total time: 100.988s

However, after rebooting the phone, the camera still clicks. The files are also still there:

$ adb shell
bluejay:/ $ ls /product/media/audio/ui/camera_click.ogg
/product/media/audio/ui/camera_click.ogg

/system/product is a symlink to /product. Why the files were not modified? How can I still remove these files?