Hi @Karthikeyan Balasubramanian and welcome to the community!
The option Enable automatic merging is available in the Branching model page for Bitbucket Server repositories (in a self-hosted instance).
From your screenshots, it looks that this is the Branching model page of a Bitbucket Cloud repository instead. Could you please confirm if this is the case?
In Bitbucket Cloud there is no such option in the Branching model page of the repositories.
There is a feature for auto-merging when builds pass, which is useful if you have merge checks (for at least X successful builds) as a requirement for merging PRs.
In order to be able to use this, you will need to first enable the Labs feature Pending merges from Labs
Afterwards, you'll need to enable this for each branch that you wish to automatically merge from Repository Settings -> Branch Permissions -> Edit/Add branch permission -> Allow automatic merge when builds pass
You can read more about how this feature works in the following blog post:
If you have any questions, please feel free to let us know.
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