Problem scenario
A user in Azure DevOps cannot approve releases to a given environment. The permissions are correct; the user is a member of the relevant custom security group in the project. Why can't the user approve the deployment to an environment?
Solution
Can the user go to the Azure DevOps organization? Can the user also see the project? The organization subsumes a project, and the organization may need to have the member be added. A parent organization may be somewhat separately from the sub-environment.
The root cause is that the permissions are not actually correct. Check the members list of the project. It could be that the user is a member of a group, but not a member of the project itself. (It may not be enough to be a member of a group in a project. The user may need to be a member of the project itself for some configurations of Azure DevOps.)
The user may not have approval authority for a relevant resource; see this posting. See also this.