Is there a rule for a noun followed by any?

I heard that a noun followed by any should be singular other than any + of a plural noun. Is this right?

Or is there no rule ? but just use singular/plural nouns followed by any?

I ask this question cause I've seen any + plural nouns quite a lot of times. ex) Do you have any plans for this summer?
The American Heritage Dictionary says:

When used as a pronoun, any can take either a singular or plural verb, depending on how it is construed: Any of these books is suitable (that is, any one). But are any (that is, some) of them available?

The Compact Oxford says:

When used as a pronoun any can be used with either a singular or a plural verb, depending on the context: we needed more sugar but there wasn't any left (singular verb) or are any of the new videos available? (plural verb)
moon7296a noun followed by any should be singular .... Is this right?
No. The noun after any can be either singular or plural, but it would have to be singular if it's an uncountable noun.

After negatives:

I don't have any books to lend you today. (book is countable)

I don't have any sugar to lend you today. (sugar is uncountable)

As the subject of a clause it's often singular:
This is so simple that any child can do it. (child is countable)

Any wine that's left over will be thrown out. (wine is uncountable)

But it can be plural as well:
Tell me if any problems arise. (problem is countable)