First, I'm wondering if some of these "details" are being floated to get the measure of public reaction.

I expect the King will arrive at the Abbey wearing Admiral's ceremonial dress (we are told) plus Garter collar and possibly Thistle sash and full red Parliamentary robes, with train and pages.

After some rituals he is divested of that garb - including his jacket - ready for the anointing. (The jacket of the uniform will not appear again until the closing procession after the Recess.)

I expect him to be reduced to a simple open shirt, and trousers of the uniform. Check this video of the coronation of George VI. Start at 18.50 and continue to the end of the anointing when we see the King wears only a simple white shirt and breeches.
I don't know what shirt is worn normally under the ceremonial dress uniform but I'm sure a shirt can be created to be suitable specifically for the anointing of King Charles - on head hands and breast.

Then begins a lot of ritual when the King is dressed in three coronation garments one by one prior to the actual crowning.

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