The3rd Earl Of Derby wrote:

Did it not occur to you to feed the shelving strips into the top or bottom
and tap it into the recess till its gone all the way down the lenght of the
side? this will then bite the sides and eliminate the paint for a truly
flush finish.

Awkward, given that both top and bottom of the bookcases had been
fitted.

...Or you could have masked the routed rebate before painting.

If I'd thought of this before painting I probably would have done. As
it is, I only thought of it later ...

John