The resource pack attached to MC-249094 offers a complete fix for this issue. Mojang have my full permission to (and are encouraged to) replace the affected vanilla model files with the contents of the resource pack.
Discovered while testing MC-249094.
The bug
The bottom of sculk shriekers, as well as the four sides, are not culled by solid blocks which are directly against them. This is due to these five faces missing cullface arguments for those faces.
How to reproduce
Place a sculk shrieker on the ground
Place four opaque blocks on each side
View the occluded sides in Spectator mode
Expected results
These faces would not render.
Actual results
They do.
How to fix
The resource pack attached to MC-249094 fixes this issue and that issue as well as offering code cleanup for readability and a reduced model file size, so I'd recommend using that model file to fix this issue rather than attempting to do so manually.
Attachments
Comments

Can also confirm that this issue is no longer present in 1.19 Pre-release 3. I'm unsure as to whether or not this is the exact fixed version though.

Confirmed 1.19 Pre-release 3 as fixed version, this issue was still present in 1.19 Pre-release 2.
Seems to be fixed in 1.19 Pre-release 3.