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I cannot shrink btrfs filesystem although there is still data and metadata space left :

$ sudo btrfs filesystem resize -11G /home;echo $?
Resize '/home' of '-11G'
ERROR: unable to resize '/home': No space left on device
1

Here are some btrfs filesystem info about /home :

$ sudo btrfs filesystem df /home | column -t
Data, single: total=92.01GiB, used=80.68GiB
System, DUP: total=8.00MiB, used=16.00KiB
System, single: total=4.00MiB, used=0.00B
Metadata, DUP: total=1.00GiB, used=631.41MiB
Metadata, single: total=8.00MiB, used=0.00B
GlobalReserve, single: total=224.00MiB, used=0.00B
$ sudo btrfs filesystem show /home
Label: none uuid: c7ee56a8-ef45-46c8-86d1-13879201a1e7
 Total devices 1 FS bytes used 81.30GiB
 devid 1 size 100.00GiB used 94.04GiB path /dev/mapper/home_VG-home

$ sudo btrfs filesystem usage -T /home
Overall:
 Device size: 100.00GiB
 Device allocated: 94.04GiB
 Device unallocated: 5.96GiB
 Device missing: 0.00B
 Used: 81.91GiB
 Free (estimated): 17.29GiB (min: 14.31GiB)
 Data ratio: 1.00
 Metadata ratio: 1.99
 Global reserve: 224.00MiB (used: 0.00B)

 Data Metadata Metadata System System 
Id Path single single DUP single DUP Unallocated
-- --------- -------- -------- --------- ------- -------- -----------
 1 /dev/dm-0 92.01GiB 8.00MiB 2.00GiB 4.00MiB 16.00MiB 5.96GiB
-- --------- -------- -------- --------- ------- -------- -----------
 Total 92.01GiB 8.00MiB 1.00GiB 4.00MiB 8.00MiB 5.96GiB
 Used 80.68GiB 0.00B 631.41MiB 0.00B 16.00KiB 

and here the output of dmesg :

$ dmesg | tail -11
[44202.411949] BTRFS info (device dm-0): new size for /dev/dm-0 is 97706311680
[44202.412156] BTRFS info (device dm-0): relocating block group 120288444416 flags 1
[44208.119721] BTRFS info (device dm-0): relocating block group 119214702592 flags 1
[44211.611669] BTRFS info (device dm-0): relocating block group 118140960768 flags 1
[44212.495603] BTRFS info (device dm-0): relocating block group 117067218944 flags 1
[44213.006830] BTRFS info (device dm-0): relocating block group 95592382464 flags 1
[44216.613870] BTRFS info (device dm-0): relocating block group 120288444416 flags 1
[44222.780073] BTRFS info (device dm-0): relocating block group 119214702592 flags 1
[44225.843279] BTRFS info (device dm-0): relocating block group 118140960768 flags 1
[44226.575236] BTRFS info (device dm-0): relocating block group 117067218944 flags 1
[44226.930918] BTRFS info (device dm-0): relocating block group 95592382464 flags 1

Can you help me ?

You're requesting the volume to shrink by 11GB, yet you only have about 6GB unallocated.

You can more efficiently use allocated extents by rebalancing the volume. Executing a command similar to btrfs balance start /home will start that process, and it may take some time to complete.

But I don't know if that will free up enough for a large amount of shrinkage.