The scene in which Palpatine and Anakin meet in TPM, and the scene with Anakin and Palpatine in his office in AOTC, were both reshoots.
We almost got a version of the trilogy where Darth Vader and the Emperor do not have a scene together until the third movie.
What a mess.
Not introducing the Chancellor/Emperor until the third film or even the OT makes a lot of conceptual sense.
ANH takes pains to set our point of view on the lowly droids before gradually working up to more powerful and politically important characters, and this is how stories often work, especially with sequels. In order to keep the audience invested it’s a good idea to leave room in the universe for powerful entities which can be slowly introduced and incorporated into the story to instill a sense of escalating stakes.
The prequels don’t do this, and this is one of the reasons they feel so flat. We are introduced to the most powerful person in the galaxy partway through the first film, which leaves no room for important character escalation. If instead Anakin had to work with Obi-wan to become a Jedi Knight through the first and second films while fighting in the Clone Wars, the meeting and potential war hero decoration of Anakin by the future Emperor in film three would feel like the culmination of the entire story.