@PRADEEP THILANKA WARAGODA Thanks for reaching out. To automate the deployment you need to create the leverage the ARM template for your deployment. This document
talks about how to Automate deployment for Azure Logic Apps by using Azure Resource Manager templates and what are the things you need to keep in mind to deploy in different environments like development, test, and production. You can leverage Azure Pipelines for continuous integration and continuous deployment (CI/CD) and this document talks more in detail.
More than one developer should be able to update the logic app.
You need to leverage the devops for the CI/CD pipeline. Developer will be building the workflow to create the ARM templates and push the changes with the updated ARM template.
The changes should be in a central repo
The ARM templates will be saved at the devops end.
Should be able to deploy to multiple environments with minimal effort
Once you have different connection strings for each environment as mentioned in the document. Once the create the devops pipeline it will be deployed to all your environment.
Update 3/30:
To develop your workflow you can leverage VS code extension (Standard logic app / Consumption logic app) to build the workflow in your local machine and once tested locally you can push the changes to DevOps. You can refer to this document for more details on how you can create workflow with single-tenant Azure Logic Apps (Standard) in Visual Studio Code. For consumption, you can refer to this document. Let me know if you have any queries or concerns. I have also updated my answer with these details.