Etymonline on "-able" doesn't expound the origin of "requiring".

-able

common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).

For example, "payABLE" literally means ABLE to pay. Ability differs from requirement. How did "payable" semantically shift to meaning 1 below?

1. (of money) required to be paid; due.

2. Able to be paid.

payables Debts owed by a business; liabilities.

payable (adj.) on Etymonline

late 14c., paiable, "to be paid, that can be or is to be paid,"
from pay (v.) + -able or from Old French paiable. From late 13c. as a surname, from the Old French word in its other sense, "of good quality."

Solution 1:

For example, "payABLE" literally means ABLE to pay.

This is incorrect. The error is shown in

late 14c., paiable, "to be paid, that can be or is to be paid,"

The meaning was always there but there was often ellipsis:

"Five pounds is now payable", can mean

"Five pounds is now payable by me to you"

or

"Five pounds is now payable by you to me"

The context will make it clear.

From the OED:

-able (suffix) Forming adjectives denoting the capacity for or capability of being subjected to or (in some compounds) performing the action denoted or implied by the first element of the compound.