The Sabba of Novardok in his sefer madregas haadom has a lengthy chapter on the idea of bitachon.
He brings it down as a machlokes between the ramban and the chovos halevavos regarding what hitadlus a person should take.
The ramban is of the opinion that no hishtadlus is necessary, so long as a person has bitachon even zero hishtadlus will yeild results. For instance, since parnassah is determined on Rosh Hashonah it does not help to work more, you will always receive the amount alloted.
The gemara says "השלך על ה" יהבך והוא יכלכלך" roughly translated as, place on hashem your burdens and he will support you. The gemara asks, what is the meaning of the word יהבך/burdens?
The gemara says, a rabbi saw an arab go by with his donkey, and the rabbi was carrying a large burden, he said to the arab, can you take my stuff, the arab said "you can place your יהבך"
From here the gemara learns that יהבך means burdens.
The vilna Gaon says, it cant be the gemara needed to find out the meaning of a word from an arab. Rather the rabbis were unsure if יהבך meant your extra burdens or even the basics that everyone would assume we should work for.
But the story with the arab illustrates that יהבך means even the basics we should place on hashem and he will provide. Because according to derech hateva there is no way an arab donkey owner would take all these goods, especially not for free. But this rabbi because of his exceptional trust had even the unnatural occur.
He also brings a story of (i think the chida) who after giving a shiur on bitachon one day, a simple worker who had attended the shiur, went home quit his job and after weeks of no food or money all of a sudden found money and became wealthy.
The students of the chida were upset, after all they had been learning about Bitachon for many years. The chida told them, this man had simple trust, he heard that g-d controls money and therefore work is pointless and he saw that as truth. You all look at it as a sugya, there is a tzad to say we need hishtadlus and a tzad to say we do not, and therefore you do not receive without hishtadlus.
He brings yaakov placing the stick before lavans animals, not as a proof of hishtadlus, rather that because it was his job to take care of lavans animals, he was required to act to the full amount.
One of the great mussar seforim writes about the presents and preparation for war, and prayer that yaakov did before going to esav. And he asks, where was his Bitachon?
He makes a distinction in the requirement of Hishtadlus, that by ones own middos having Bitachon is not enough, and since yaakov felt a little fear he had to do hishtadlus.
According to the Saba, even the chovos halevavos would agree that for the one who exceedingly trusts no histadlus is required, but for other Hihtadlus is.