The simplest answer is that the English verbal doesn't come from the English verb.
They both have a common root in the Latin verbum, word, but came to English via different routes, and took on slightly different meanings in the process. And the Latin verbum means both word and verb, thanks to Greek.
According to the Oxford English Dictionary, the first-known example of verb is from around 1397 in the prologue to the Old Testament in Wycliffe's' Bible:
Sumtyme it mai wel be resoluid into a verbe of the same tens.
Its etymology is fairly straightforward: English verb comes from either Old French verbe or Latin verbum, meaning both word and verb (more on this later!).
The first-known use of verbal is in Caxton's 1483 translation of Chartier's Le Curial:
We be verbal, or ful of wordes, and desyre more the wordes than the thynges.
Verbal means dealing with words, and this example also illustrates how it, according to the OED, especially refers to people who deal in mere words rather than things or realities.
English verbal also comes from Old French or Latin; either verbal or verbālis: consisting of words, pertaining to verbs. This comes from the shared root verbum, word and verb.
Part of the reason why we have verb for action words and verbal for words is because the Latin verbum means word in general, but also the subcategory of words expressing action, as opposed to those expressing names, nomen, name or noun.
This dichotomy is derived from Greek rhēma ("saying, utterance, word, verb") and onoma ("naming"). In the Sophist, Plato defined verbs (rhemata) as applied to actions, whilst names (onomata) are applied to those which perform those actions.
Of course, 500 and 600-year-old words don't survive for so long with a single meaning.
Verb has also referred to "the most-important thing" and to "word", although these are obsolete.
Verbal is more productive. The OED has seven senses as an adjective (with 18 sub-definitions), and five as a noun.
As an adjective, it refers to talkative people and people interested in the mere words of a composition; of things composed of words, and of the nature of a word; to detailed reports; to things only affecting words, or only expressed in words, or only consisting in words or speech; and expressed in speech rather than writing, or people using spoken words; and word-for-word; and things derived from a verb.
As a noun verbal can refer to nouns derived form a verb; a collection of words, a dictionary; words performing the role of a verb; a damaging verbal statement; and abuse.
So those verbal adjectives are more wordy whilst the nouns are more verby.