Add bridge zombienet test back to the CI (#3264)

Related to https://github.com/paritytech/polkadot-sdk/issues/3176

This PR only adds the first bridge zombienet test back to the CI after
fixing it, reverting
https://github.com/paritytech/polkadot-sdk/pull/3071

Credits to @svyatonik for building all the CI infrastructure around
this.