According to suggestions in the media, the King could arrive at the Abbey wearing Admiral's ceremonial uniform, instead of tunic, breeches and stockings worn by kings at past coronations. This has a bearing on just how the anointing can be on hands, head and breast.

I think HM might also wear the Garter collar and possibly Thistle sash and full red Parliamentary robes, with train and pages.

After some rituals he is divested of that garb ready for the anointing. I'd expect also the jacket of the uniform to be removed and not appear again until the closing procession after the Recess.

I expect HM 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 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.