1) launched focal lxd container
2) enabled proposed
3) installed the v5.15 based kernel
apt install linux-generic-hwe-20.04-edge
4) disabled proposed

5) observed that it fails to install 

# apt install rtl8812au-dkms=4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.3
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following NEW packages will be installed:
  rtl8812au-dkms
0 upgraded, 1 newly installed, 0 to remove and 34 not upgraded.
Need to get 1116 kB of archives.
After this operation, 8906 kB of additional disk space will be used.
Get:1 http://archive.ubuntu.com/ubuntu focal-updates/universe amd64 rtl8812au-dkms all 4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.3 [1116 kB]
Fetched 1116 kB in 1s (1761 kB/s)      
Selecting previously unselected package rtl8812au-dkms.
(Reading database ... 79023 files and directories currently installed.)
Preparing to unpack .../rtl8812au-dkms_4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.3_all.deb 
...
Unpacking rtl8812au-dkms (4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.3) ...
Setting up rtl8812au-dkms (4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.3) ...
Loading new rtl8812au-4.3.8.12175.20140902+dfsg DKMS files...
It is likely that 5.13.0-40-generic belongs to a chroot's host
Building for 5.15.0-25-generic
Building initial module for 5.15.0-25-generic
Error! Bad return status for module build on kernel: 5.15.0-25-generic (x86_64)
Consult /var/lib/dkms/rtl8812au/4.3.8.12175.20140902+dfsg/build/make.log for more informati
on.
dpkg: error processing package rtl8812au-dkms (--configure):
 installed rtl8812au-dkms package post-installation script subprocess returned error exit s
tatus 10
Errors were encountered while processing:
 rtl8812au-dkms
E: Sub-process /usr/bin/dpkg returned an error code (1)

6) enabled proposed once again

7) observed that from proposed does not build and install fine.... it seems that despite being in a chroot and requesting to build against v5.15 kernel it tries to build against the host kernel:

Unpacking rtl8812au-dkms (4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.4) over (4.3.8.12175.20
140902+dfsg-0ubuntu13~20.04.3) ...
Setting up rtl8812au-dkms (4.3.8.12175.20140902+dfsg-0ubuntu13~20.04.4) ...
Loading new rtl8812au-4.3.8.12175.20140902+dfsg DKMS files...
It is likely that 5.13.0-40-generic belongs to a chroot's host
Building for 5.15.0-25-generic
Building initial module for 5.15.0-25-generic
ERROR: Cannot create report: [Errno 17] File exists: '/var/crash/rtl8812au-dkms.0.crash'
Error! Bad return status for module build on kernel: 5.15.0-25-generic (x86_64)
Consult /var/lib/dkms/rtl8812au/4.3.8.12175.20140902+dfsg/build/make.log for more informati
on.
dpkg: error processing package rtl8812au-dkms (--configure):
 installed rtl8812au-dkms package post-installation script subprocess returned error exit s
tatus 10
dmesg: read kernel buffer failed: Operation not permitted
                                                         Errors were encountered while proc
essing:
 rtl8812au-dkms
E: Sub-process /usr/bin/dpkg returned an error code (1)
root@normal-snake:~# cat /var/lib/dkms/rtl8812au/4.3.8.12175.20140902+dfsg/build/make.log
DKMS make.log for rtl8812au-4.3.8.12175.20140902+dfsg for kernel 5.15.0-25-generic (x86_64)
Wed Apr 27 15:22:31 UTC 2022
make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/5.13.0-40-generic/build M=/var/lib/dkms/rtl8812au/4.3.8.12175.20140902+dfsg/build  modules
make[1]: *** /lib/modules/5.13.0-40-generic/build: No such file or directory.  Stop.
make: *** [Makefile:1457: modules] Error 2

this needs to be verified in a VM. And the bug that dkms module is not built against requested kernel version should be filed and fixed separately.