Hopefully

adv.hopeful, calmwarm

Meaning 1

With a sense of hope or positive expectation.

Reach for it when describing a person's hopeful manner or expression

The children looked hopefully toward the clearing sky.

everyday
eagerly
enthusiastic desire shows in the waiting
not when Eagerness adds impatience or excitement that hopeful attention may lack.
warm
with hope
plain phrasing should preserve emotional sincerity
not when The phrase is less smooth when modifying a quick physical action.
professional
optimistically
a favorable outlook shapes the person's approach
not when Optimistically can imply a reasoned forecast rather than an emotional manner.
literary
expectantly
visible attention is fixed on something likely to arrive
not when Expectation may be neutral and stronger than mere hope.

Used to express a wish that something will happen.

Reach for it when softly stating a desired future outcome without claiming it will occur

Hopefully, the repaired lift will reopen before Monday.

playful
with luck
chance clearly influences the desired result
not when Hope may rest on effort or evidence, not luck.
everyday
if all goes well
a practical wish acknowledges possible obstacles
not when This phrase foregrounds conditions and can sound cautious rather than hopeful.
formal
it is hoped
impersonal wording suits an official statement
not when The passive construction hides who holds the hope.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.