Just to clarify - the original Star Trek will appear less advanced in terms of its designs and aesthetic compared to the other Star Trek shows we have watched so far, but this is only due to the limitations of television production at the time. This is not “true” in story terms - the technology and society in TOS should be read as on par with Discovery and Strange New Worlds, which all take place at roughly this point in the timeline, and the Enterprise, despite looking different, should be accepted as the exact same ship Pike commanded in Strange New Worlds.
As for the actual viewing order, to fully appreciate the development of the show, it's recommended to watch TOS in production order instead of by air date. In general, don’t get too hung up on continuity with the rest of the franchise in these early days - they take quite a while to pin some stuff down that the rest of the franchise takes for granted.