I've set up an upgrade on the XPerience plugin to increase the backpack capacity. The XPerience plug-in also prompts for increased capacity. However, the actual opening of the backpack, the backpack capacity did not increase.

I have found the reason.

Edit: Looks like you solved it as I was typing.

The XPerience plugin grants increased capacity by simply granting permissions. However, since a few Backpacks versions ago, the backpack permissions are dynamic according to the plugin configuration, so it's possible for there to be a desync where XPerience tries to grant permissions that do not exist or skips permissions that do exist.

This help thread should be opened with the XPerience dev, not with the Backpacks dev, since the XPerience dev owns the integration.

As far as troubleshooting possible on your side, you can check the XPerience docs and config for any instructions or options related to Backpacks, check your Backpacks config, and check any permissions you have been granted via a permissions manager plugin. If you are certain you have been granted the correct permission but are not seeing the corresponding size, then you might have a dynamic size profile permission granted to you which will supersede the standard permissions, in which case you should revoke such permissions.