Overwhelmed vs Be overwhelmed?

I am confused about the following sentence:

They were overwhelmed with work vs They were overwhelmed by work vs Work overwhelmed them.

Is overwhelmed used(in first two sentences) as a verb(passive) or an adjective?

Can the word By be used in a same way like with in passives?

If it’s a passive voice, then who is the agent and patient?

Below sentence is also like above,

They were overwhelmed with joy.

Please help me out!

Sometimes, I get confused identifying passive and past participle adjective.

Thanks!