How to resize my system without destroy data and efi?

How to move my system to the left-hand side included the unallocated area.

If it’s impossible, what if I make a snapshot backup, erase entire systems then restore the in the new installation system?

Unlike legacy boot, the efi boot doesn’t have any direct physical addresses for boot stages (other than the GPT itself knowing where the partitions are).

So if /boot/efi were not mounted then gparted could move it, and everything would still work.

If you boot into some other system (USB stick etc.) that contains gparted then your btrfs would not be mounted, allowing gparted to grow it into the free space that would be before it after the efi partition was moved.

None of that should damage data or efi. The only issue is that it must be dismounted while moving it.

You do not even have to boot into the live usb to relocate /boot/efi since that partition is not normally actively in use once booted.

Simply boot as normal then umount /boot/efi.
Once it is no longer mounted then use gparted to move that partition to the left.
Once that partition is moved then you would be able relocate/extend the main linux system. That part would require that you boot to a live usb since gparted will not work on a mounted file sytem.