Based on your issue description, you want to read WebApp connection string credentials from Keyvault, it is a recommended approach.
I believe you have hosted the Azure WebApp on an Azure App Service, if you have provisioned your webapp on some other Azure service please let me know.
Yes, you can use Azure Key Vault to store your database password and retrieve it in your web app. You can follow the steps in this tutorial to configure your Azure web app in an ASP.NET Core application to read a secret from your key vault.
Here are the high-level steps you can follow:
1. Create an Azure Key Vault and store your database password as a secret in the key vault.
2. Grant your web app access to the key vault.
3. Modify your web app to access the key vault and retrieve the secret.
Checkout this doc for more info: Tutorial: Use a managed identity to connect Key Vault to an Azure web app in .NET
Additionally, In Azure App Service, app settings are used to store configuration values that are passed to your application as environment variables. You can use app settings to store a wide range of configuration values, such as database connection strings (in your case), API keys, and other secrets.
App settings can also be resolved from Key Vault using Key Vault references. See this doc section for more info: Configure app settings.
Kindly let us know how it goes, we will follow-up with you further.