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.
I forgot the most crucial thing. So the 立ち上がる is but an ordinary intransitive verb "to stand up".