basically, to give you a rundown on why it becoming bizarre at the end is the reason the game is so good.
it opens with your expectations of Metal Gear Solid, you playing as Snake doing things like in MGS1, which is what the first part of the ruse is. But then part 2 comes, which is meant to be a recreation of the shadow moses incident, with Raiden playing the part of Snake, much like what is expected for a sequel.
But it's not, Raiden isn't Snake. But he plays almost exactly the same and fills the same role. But they're not the same. Even similar things aren't the same, like you fighting a Harrier and not a Hind. The fantastical is increased further, with the shamans and psychics of MGS1 replaced with a literal vampire and a woman who's so lucky she cannot be hurt (Which the game tries subverting, but still gives the whiff of it being there). Notably, Vamp himself is a callback to Liquid Snake never strawberry floating dying.
This recreation could be called as an attempt to create an in universe sequel, but it's not quite right, there's things missing and not right. The foremost being the protagonist for part 2 onwards, Raiden. He's set up as the protagonist replacing the 'dead' Snake, and his actor in the recreation. However, despite Raiden himself getting into the Snake role (even taking his name for a short while), he's definitely not Snake. He's a stand in for the player themself, a person living vicariously through videogames, pretending they're someone they're not. In Raiden's case, he thinks of himself as a legendary soldier, despite his only experience being VR, essentially videogames. Both Raiden and Player had fond memories of experiencing Shadow Moses themselves, despite not being there, they felt like they were. But, Raiden is controlled by the player and controlled to his whims, right down to his dogtags having your name on them.
Towards the end of the game, when it starts getting more bizarre, is when Raiden finally asserts his difference from Snake. You could also say it's when MGS2 asserts its difference from all the callbacks to MGS1. Raiden's use of a sword also represents this, a weapon that Snake has never used. At this point too, the facade also breaks down. The Colonel starts freaking out, as Raiden is breaking free from the recreation and the game is breaking free of the shackles of being a sequel. He, and the player wanted to believe it was the real Roy Campbell, since that was 'MGS1' in their eyes. The recreation/game/Patriot AI doesn't like that everything is not going as it should and it starts freaking out and getting weirder, such as the locations being named from the actual body parts.
Even with all these deviations, the final nail in the coffin is Solid Snake himself arriving, fully distinct from Raiden. Raiden is a man running with a sword, a weapon unique to him from Snake, whilst Snake is as he is in the player/Raidens memory. Raiden's fully differentiated himself and MGS2 is no longer a retread of MGS1, you're now playing the game differently.
The game finally sheds MGS1 after this when Liquid takes over Ocelot, taking the RAY and legging it, with Snake in hot pursuit, just leaving Solidus and Raiden together, everyone from the prior game dead or having left. And at the end of the game, when you no longer have control, Raiden sheds his Dog tags with you on, moving on from both the game and MGS1.
tldr MGS2 is set up to be a by the numbers sequel, but it and Raiden manage to break free of being just rehashes of their prior incarnation and make something unique for themself.