Environment:

• fabric 1.19.2-0.14.21
• fabric-api 0.76.0
• modernfix 3.6.0
• continuity 2.0.2

config/modernfix-mixins.properties
mixin.perf.dynamic_resources=true

config/continuity.json

{
  "connected_textures": true,
  "emissive_textures": true,
  "custom_block_layers": true,
  "use_manual_culling": true
}

Resource pack order:

1. continuity/glass_pane_culling_fix
2. continuity/default
3. Fabric Mods
4. vanilla

Screenshot:

Known issue, I'm waiting on the Continuity developer to have some time to work towards a compatibility solution.

This issue has been fixed for 1.19.4+. For 1.18.2 & 1.19.2 you will need to choose between having connected textures and enabling dynamic resources. A warning is now displayed if both are used.