No, so is not interchangeable with because in those sentences.
Their meanings are related and they both serve to mark a reason but let's look at your example.
My car is broken so I am going to the garage
I am going to the
garage because my car is broken
Both sentences express exactly the same meaning but notice where is the reason located in each one.
REASON so ACTION
ACTION because REASON
In the quoted text, first the handle got stuck and that's the reason why later she was forced to open the suitcase.
She was forced to open the suitcase because previously the handle
The handle got stock previously so she was force to
open the suitcase
[previously = when she got off the car]
Additional information about the use of so in the Cambridge Dictionary.
WARNING: I don't mean that you can ALWAYS, IN EVERY CASE, swap the order of the clauses and replace "so" by "because". I was just using the examples provided in the original question, simplifying them in an effort to explain the use of those conjuctions. Please check the provided link, there are cases like the one exposed by @Astralbee where you CAN NOT reorder the clauses in such way.
I've been pointed by @Astralbee that my reasoning is wrong but the Cambridge Dictionary entries related to so and therefore seems to back me up
and for that reason; therefore:
because of that; for that reason
Please, notice the presence of the determiner that, it refers to something that has been PREVIOUSLY mentioned. USUALLY when you use so, the reason, the cause, has appeared before. The quoted text of the OP fullfils this structure.
got stuck BEFORE had been opened
But let's check what because means
for the reason that
According to the dictionary, USUALLY the reason is explained AFTER because. All depends on where that is located in these definitions.