Check if a git tag is pushed with related commit

I need to check automatically if a TAG has been pushed on remote, if the commits related with the commit has been pushed and if the TAG/commit is on a specific branch.

Currently I'm using git ls-remote but I can just check if tag is pushed or not. Not enough.

I tried to clone locally the repository with git clone --branch to get specific TAG, however in this way I can't have information about the branch where TAG is, if I use the command git branch the output is just

* (no branch)

Do I need to clone the repository? How can I clone the repository without the whole history just to perform this kind of check?

You could try git branch -a --contains $tagname or git branch -r --contains $tagname. tagname could also be HEAD in your case. But still, you need to clone the whole history because the tagged commit could be reachable from multiple branches, and without the whole history we cannot precisely find out what exactly these branches are. If you don't want to clone it every time, you could keep a repository and fetch all tags and branches first before checking if a tag is contained by a branch.

An alternative is to run a service, like a Django service, on the server that hosts the remote repository. It could also be on a server that hosts a mirror repository that syncs with the remote repository constantly. Send a request to the service. The service finds out the branches that contain the tag/commit in the hosted repository that has the whole history, and then returns the result.