Synchronize templates through PRs, instead of pushes (#5291)

Despite what we had in the [original
request](https://github.com/paritytech/polkadot-sdk/issues/3155#issuecomment-1979037109),
I'm proposing a change to open a PR to the destination template
repositories instead of pushing the code.

This will give it a chance to run through the destination CI before
making changes, and to set stricter branch protection in the destination
repos.