Ansible Engine itself, ansible-playbook from the ansible package, provides a means to access hosts remotely and run modules on them. That's it, the core tool does not have an API. Adding more features like approval or role based access controls implies adding components on top. Possibly take advantage of tools you may already use.
ansible-runner is the API to Ansible that powers AWX, abstracted into a library and container image. Consider it for scripting Ansible. If you were wondering why there is no official ansible container image, this is it.
A relatively simple case is just running ansible-playbook. Playbook development is approved via whatever collaborative change control process. Then someone manually logs into the bastion/management host, fetches the approved playbook from version control, and runs that exact tag. Simple, no extra components to set up. But lacks strict controls over what exactly gets run. Not trivial to make the playbook immutable to whomever is running them, still need to trust the person.
Version control oriented continuous delivery pipeline could fit your workflow. Full featured forges like GitLab can require approvals to merge requests. On approval, the resulting playbook is automatically run on a pipeline worker with ansible-runner. Workers are what remotes into hosts of the environment, via ssh. Strong controls that the version approved is what runs. However, this style of pipeline is optimized for a developer experience, and maybe not great at scheduled runs of the same thing.
Any ops tool that can run arbitrary scripts can run playbooks. Rundeck or Jenkins may not be full featured development hubs, but running things on triggers is their core competency. Again consider ansible-runner as the environment to execute Ansible in.
And there are Ansible specific web interfaces, primarily AWX or Semaphore. AWX is fairly complex, a thing to do all things Ansible for any size enterprise. Semaphore is a bit simpler. Being Ansible specific can be an advantage. But by no means are they they only alterative to interactive Ansible at the terminal. Your organization may prefer other tools for developing, approving, and running things.
