As far as the Eagle and Constellation go, we have no proof either are Constitution-class. The Eagle was never seen on screen. The Constellation was identified as 'Starship Class', but the AMT model used for it was quite a bit different from the Enterprise filming model.
If one wants them all to be Connies, there's nothing wrong with it.
If one wants them to be other ships that were upgraded to Connie specs, there's nothing wrong with it.
If one wants to treat them as an entirely different class(es), there's nothing wrong with it.
If one wants to treat the Oberth-class as an older ship type, there's nothing wrong with it.
If one wants to treat the Oberth-class as a new build in The Search for Spock, there's nothing wrong with.
Because nothing on film contradicts any of the above.