OpenWRT on x86_64 does not use overlay mounts, here's an overview of a current instance running in a Proxmox-managed container:
/dev/mapper/pve-vm--500--disk--0 on / type ext4 (rw,relatime,stripe=512)
none on /dev type tmpfs (rw,relatime,size=492k,mode=755,uid=100000,gid=100000,inode64)
proc on /proc type proc (rw,nosuid,nodev,noexec,relatime)
... more proc mounts...
sysfs on /sys type sysfs (ro,nosuid,nodev,noexec,relatime)
... more sysfs mounts
fusectl on /sys/fs/fuse/connections type fusectl (rw,nosuid,nodev,noexec,relatime)
udev on /dev/net type devtmpfs (rw,nosuid,relatime,size=65960672k,nr_inodes=16490168,mode=755,inode64)
none on /sys/fs/cgroup type cgroup2 (rw,nosuid,nodev,noexec,relatime)
lxcfs on /proc/cpuinfo type fuse.lxcfs (rw,nosuid,nodev,relatime,user_id=0,group_id=0,allow_other)
... more lxcfs mounts
udev on /dev/full type devtmpfs (rw,nosuid,relatime,size=65960672k,nr_inodes=16490168,mode=755,inode64)
... more udev mounts
devpts on /dev/pts type devpts (rw,nosuid,noexec,relatime,gid=100005,mode=620,ptmxmode=666,max=1026)
... more devpts mounts
none on /proc/sys/kernel/random/boot_id type tmpfs (ro,nosuid,nodev,noexec,relatime,size=492k,mode=755,uid=100000,gid=100000,inode64)
tmpfs on /tmp type tmpfs (rw,nosuid,nodev,noatime,uid=100000,gid=100000,inode64)
No overlays, just a normal ext4 filesystem. Data in /etc is stored in /etc, data in /var is stored in /var, etc. OpenWRT running from a filesystem image is 'just another Linux distribution which happens to run the same software as that re-flashed router'.