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".
"を手に立ち上がる"
yields 100k hits and 210 results if you go to the last page, a search for"を手に立ち上"
yields only 11 hits...