Boot from an .img device (a copy of the physical device)

There is a copy of the disk in IMG format:

root@linux /mnt # fdisk -l /mnt/output.img 
Disk /mnt/output.img: 3 GiB, 3221225472 bytes, 6291456 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: gpt
Disk identifier: 3EEB19F8-AB57-47B4-A7E7-F2A0BDE6C2B1

Device           Start     End Sectors Size Type
/mnt/output.img1  2048    4095    2048   1M BIOS boot
/mnt/output.img2  4096 6289407 6285312   3G Linux LVM

lvdisplay provides the following information about the disk:

lvm> lvdisplay
  --- Logical volume ---
  LV Path                /dev/connect/root
  LV Name                root
  VG Name                connect
  LV UUID                KXxms1-2d0j-C8Ps-6azt-3U0z-PpOO-K9mS0B
  LV Write Access        read/write
  LV Creation host, time client-dev-building-02, 2024-07-25 13:36:12 +0300
  LV Status              NOT available
  LV Size                2,00 GiB
  Current LE             512
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto
   
  --- Logical volume ---
  LV Path                /dev/connect/boot
  LV Name                boot
  VG Name                connect
  LV UUID                OKFDNN-IUDQ-a0Ol-6Dqg-lDKu-GIWK-4A8faP
  LV Write Access        read/write
  LV Creation host, time client-dev-building-02, 2024-07-25 13:36:14 +0300
  LV Status              NOT available
  LV Size                512,00 MiB
  Current LE             128
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto
   
  --- Logical volume ---
  LV Path                /dev/connect/home
  LV Name                home
  VG Name                connect
  LV UUID                Uls6Oa-fQ64-Qrpd-mVXr-kYxo-PZmO-uxXx4Z
  LV Write Access        read/write
  LV Creation host, time client-dev-building-02, 2024-07-25 13:36:14 +0300
  LV Status              NOT available
  LV Size                508,00 MiB
  Current LE             127
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto

I created a USB stick with GRUB download. I copied the file output.img there. My configuration looks like this:

menuentry "output" {
        insmod lvm
        set isofile="output.img"
        loopback loop (hd0,2)/${isofile}
        linux (lvm/connect-boot)/vmlinuz root=/dev/connect/root ro
        initrd (lvm/connect-boot)/initrd.img
}

The kernel is loaded, but when loading initramfs it is not possible to mount the root directory, it gives an error:

Begin: Loading essential drivers ... done.
Begin: Running /scripts/init-premount ... done.
Begin:  Mounting root file system ... Begin: Running /scripts/local-top ... Volume group "connect" not found
  Cannot process volume group connect
done.

I mean, initramfs lacks LVM boot support.

Is there any way to mount the root directory, or load to GRUB, which is available on output.img?

My attempts to boot directly from the LVM device gives the error unknown file system type LVM2_member

enter image description here

It is necessary to load it in this form, without writing IMG directly to USB. The output.img file is always different, so i need to make different boot options from different disks in this format.