Reference:
https://docs.microsoft.com/en-us/azure/devops/notifications/oob-supported-event-types

Instead pass the HTTP trigger payload into an Azure Service Bus queue to be processed by a queue trigger function and return an immediate HTTP success response.
Note: Large, long-running functions can cause unexpected timeout issues. General best practices include:
Whenever possible, refactor large functions into smaller function sets that work together and return responses fast. For example, a webhook or HTTP trigger function might require an acknowledgment response within a certain time limit; it's common for webhooks to require an immediate response. You can pass the HTTP trigger payload into a queue to be processed by a queue trigger function. This approach lets you defer the actual work and return an immediate response.
Reference:
https://docs.microsoft.com/en-us/azure/azure-functions/functions-best-practices

Instead update the web.config file to include the applicationInitialization configuration element. Specify custom initialization actions to run the scripts.
Note: Some apps might require custom warm-up actions before the swap. The applicationInitialization configuration element in web.config lets you specify custom initialization actions. The swap operation waits for this custom warm-up to finish before swapping with the target slot. Here's a sample web.config fragment.
<system.webServer>
<applicationInitialization>
<add initializationPage="/" hostName="[app hostname]" />
<add initializationPage="/Home/About" hostName="[app hostname]" />
</applicationInitialization>
</system.webServer>
Reference:
https://docs.microsoft.com/en-us/azure/app-service/deploy-staging-slots#troubleshoot-swaps