How to use a slash to describe two options, one of which is made up of two or more words?

The FAQ of the Chicago Manual of Style advises:

If the slash divides two words, there is no space. If it divides two phrases or sentences (or a single word from a phrase), it requires a space before and after. Please see CMOS 6.106.

Since knowledge base constitutes a phrase, you are correct about padding the slash with spaces:

Please consult our handbook / knowledge base

All the possibilities you envisage are bound to be ambiguous for at least some of the readers, although the last solution of using spaces appears rather good.

There is the alternative of using a hyphen: handbook/knowledge-base; hopefully the readers would make the difference with "handbook-/knowledge-base".

Note: hyphens are used freely enough in English and they tend to be used increasingly.

There is an ambiguity in using the "/". It may connect the alternative forms of your information as a handbook (which, for example, might be paper) and as a knowledge base (which might be digital).

If this is the case, I suggest not using "/". It may be easily replaced by "handbook or knowledge base" or (even better, with no ambiguity) by "knowledge base or handbook"

Or does "/" merely connect the names of your information, being one thing that you describe with either of two names (for example, your handbook is only published online and you also describe it as your online knowledge base)?

In this case why use two names for the same thing? Better to use one name and not confuse the reader.