Is "Drawn" adjective or verb in "Beth felt strangely drawn to this gentle stranger"

Drawn is the past participle of the verb draw, meaning pull.

Although we draw the curtains, and ride in horse-drawn carriages, we also use draw metaphorically to mean "bring (a crowd, an audience, etc.) by inducement or attraction" (Lexico). For example, "His music drew the crowds."

Hence draw can be used to mean attract: His hat drew our attention.

Beth felt strangely attracted to this gentle stranger.

1.75 million Google hits for "felt let down" and 625 000 for "felt let down by" would seem to confirm that these usages, both the intransitive (possibly about 1.1 million hits) and the transitive, are, as I'm sure most would intuitively agree, idiomatic. And in this case, 'let down' is seen as a multi-word ('phrasal') verb rather than an adjective by most dictionaries, for instance Cambridge Dictionary:

let down someone — phrasal verb with let verb [T]

to cause someone to be disappointed, often because you have failed to do what you promised

and Farlex Dictionary of Idioms:

let down

... In all usages as a verb, a noun or pronoun can be used between "let" and "down."

2. [verb] To fail or disappoint someone; to neglect or be unable to do what was wanted, required, or promised to someone.

• Dad said he'd be here to watch my baseball game, but he let me down again.
• We're counting on you to close this deal, Robert—don't let down the firm.

So is it legitimate to use a verb after "feel"? Yes. But not all verbs. here is a list of Google hits for various "felt V-ed by" strings:

• "felt let down by" 625 000
• "felt hurt by" 375 000
• "felt slighted by" 255 000
• "felt insulted by" 150 000
• "felt loved by" 147 000
• "felt neglected by" 66 000
• "felt appreciated by" 27 000
• "felt overlooked by" 18 000
• "felt diminished by" 9 500
• "felt hated by" 5400
• "felt liked by" only 2400, often negative polarity ( ... never really felt liked by ...')
• "felt favoured by" 350
• "felt esteemed by" 250
• "felt detested by" 175
• "felt abhorred by" 175

With the low-popularity strings, fuller expressions ('felt that they were liked by', 'felt as though he was detested by' etc) sound more natural.

For comparison, we have

• "felt drawn to" 1 250 000
• "felt strangely drawn to" 58 000
• "felt drawn towards" 270 000
• "felt attracted to" 340 000

This supports the claim that feel can take part in certain [feel] + [past participle + preposition/particle] strings, including 'feel {strangely} drawn to'.

In English, the passive voice uses the auxiliary verb be (or sometimes get). Thus "Beth was drawn by the stranger" (or "Beth got drawn by the stranger") could be a passive construction. But "Beth felt drawn" is not.