In Vim, how do you search for a word boundary character, like the \b in regexp?

/the\>

See :help /ordinary-atom

I assume "regexp" means PCRE. It is worth noting that Vim's regex syntax differs from (and apparently predates) PCRE.

See also:

Why does VIM have its own regex syntax?
What's the difference between vim regex and normal regex?
Within vim's regex engine, why are some metacharacters escaped and some are not?
Can I make vim accept \b rather than just \< and \>?

Use \< and \> for word start and word end, respectively.

E.g. In your specific case you would use:

/the\>/

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