It's not the PM's plane. Trump has his own, as do quite a few other leaders, but this one is a multipurpose plane and is actally pretty basic.
From your own link "The plane used by Boris Johnson and members of the royal family for international travel is being repainted in the colours of the Union flag to "better represent" the UK abroad."
How would it look if the PM or Royal Family went in the plane on a trade mission saying what the UK can offer with paint peeling off, maybe an EU logo on it, and in need of general maintenance. Branding is a key part of marketing. Is it wasted money when any company advertises or rebrands itself or any department store gets spruced up?