EDIT: I just read that older Standard App Services do not support VNET Integration - only newer ones built on Standard or Premium V2 do. Which means even upgrading from an old Standard S1 might cause an issue - likely what you're seeing.
The feature is available from all App Service scale units in Premium
V2 and Premium V3. It's also available in Standard but only from newer
App Service scale units. If you are on an older scale unit, you can
only use the feature from a Premium V2 App Service plan. If you want
to make sure you can use the feature in a Standard App Service plan,
create your app in a Premium V3 App Service plan. Those plans are only
supported on our newest scale units. You can scale down if you desire
after that.
See below for more information. Copied from the Github issue for easier reference.
If your app runs in an App Service deployment where PremiumV2 isn't
available, or if your app runs in a region that currently does not
support PremiumV2, you will need to re-deploy your app to take
advantage of PremiumV2. You have two options:
Create a new resource group, and then create a new app and App Service
plan in the new resource group, choosing your desired Azure region
during the creation process. You must select the PremiumV2 plan at the
time the new app service plan is created. This ensures the combination
of resource group, App Service plan, and Azure region will result in
the App Service plan being created in an App Service deployment that
supports PremiumV2. Then redeploy your application code into the newly
created app and app service plan. If desired you can subsequently
scale the App Service plan down from PremiumV2 to save costs, and you
will still be able to successfully scale back up again in the future
using PremiumV2.
If your app already runs in an existing Premium tier, then you can
clone your app with all app settings, connection strings, and
deployment configuration into a new app service plan that uses
PremiumV2. In the Clone app page, you can create an App Service plan
using PremiumV2 in the region you want, and specify the app settings
and configuration that you want to clone.
Also this from the same Microsoft Documentation says:
The feature is available from all App Service scale units in Premium
V2 and Premium V3. It's also available in Standard but only from newer
App Service scale units. If you are on an older scale unit, you can
only use the feature from a Premium V2 App Service plan. If you want
to make sure you can use the feature in a Standard App Service plan,
create your app in a Premium V3 App Service plan. Those plans are only
supported on our newest scale units. You can scale down if you desire
after that.
Also more information about incompatible Resource Group and App Service SKU combination. You will note that this documentation has already changed it to Premium v3
Original Answer
So Microsoft clearly says that a Standard plan falls in scope for VNET Integration support. And as you rightly pointed out:
The VNet Integration features:
Require a Standard, Premium, PremiumV2, PremiumV3, or Elastic Premium
pricing plan.
You do not need to upgrade to another plan.
