You can check out Deployments - List rest api to get the currently deployed release id.
You can use the query parameters to query the currently deployed release id of a specific stage of a specific release pipeline.
See below example: Using additional parameters definitionId,deploymentStatus,definitionEnvironmentId(ig.stage id.),$top
`https://vsrm.dev.azure.com/org/proj/_apis/release/deployments?definitionId=3&deploymentStatus=succeeded&definitionEnvironmentId=5&$top=1&api-version=6.1-preview.2`
Note: You can get the definitionId, definitionEnvironmentId from the url of the releae pipeline.

If you are using powershell script to call above rest api. You need to escape the $ in $top parameter by adding a back tick "`$top".