A を B に
is a common literary adverbial expression that means with A in/on B, literally or figuratively.
In most cases you have a part of body in B, as 小銭を手に
with coins in hand, 期待を胸に
with expectation in chest (= heart), ドアを背に
with door in back (= with back against the door), リュックを(背/肩)に
with backpack on shoulder etc.
But it's also frequently used with position/moment words in B, notably 心配をよそに
with concern in elsewhere (= much to others' unease), 敵を前に
with enemy in front (= confronting one's enemy), その手紙を最後に
with the letter at the end (= no contact since the letter) etc.
snailboat's analysis isn't wrong, but you can't expect ~に and ~にして to be used interchangeably in real life, because:
ゴミ袋を手に立ち上がる to stand up with garbage bag in hand
ゴミ袋を手にして立ち上がる to stand up after grasping the garbage bag
~にして contains a verb te-form, thus always describes two motions occurring in succession, but not concurrently.
Here is a Japanese thesis about the difference between AをBに with and without して. You can also find more examples of this construction, which I didn't cover here.
P.S.
I forgot the most crucial thing. So the 立ち上がる is but an ordinary intransitive verb "to stand up".