Recognition test: the verb acts as a helper before a bare main verb and takes no -s ending. She would leave soon. Yes, would is a modal verb.
Recognizing modal verbs
Core modal: a helper with no -s ending and no to before the next verb. She can swim. Clue: third person still says she can, never she cans.
Core modal with past form: same helper behavior, plus a past-shaped partner. He could read at five. Clue: could pairs with bare read just as can does.
Core modal for hypothesis: helper before a bare verb, marking imagined or expected situations. That would be nice. Clue: would never sits next to to (she would to go is wrong).
Semi-modal: helper-like meaning but it behaves like an ordinary verb in some ways, often keeping to (sometimes taking endings). She ought to rest. Clue: ought keeps to and has no bare-verb partner, so it fails the strict test; this does not change the answer about would.
Ordinary main verb: takes endings and follows helpers. She helps daily. Clue: helps shows -s, something no modal ever shows.
Why would is not a semi-modal
Refine the test with one boundary question: does the verb keep its helper shape everywhere? A core modal never takes -s, never takes to, and works as the only helper before the main verb.
Would passes all three checks: she would go, never she woulds or she would to go. Contrast a semi-modal like ought to, which keeps to and cannot pair with a bare verb alone.
Semi-modals such as ought to, used to, need, and dare sit near the boundary because they share helper-like meaning but keep to or inflect like ordinary verbs. Since would fails none of the checks, it stays on the modal side of the line.
One caution: some modals have exceptions with to, so treat the three checks as a working test, not a flawless rule. For would specifically, the three checks settle it. It works as a helper verb with a bare main verb, as in she would go, and that puts it firmly on the modal side of the line.