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Currently, I have two examples in my mind:

• Halo (Halo video game series; 2001): Can destroy all sentient life within three galactic radii




• The Moment/ Eye of Discord/ Galaxy Eater (Doctor Who (2005) TV series; 2013): Can destroy entire galaxy within a moment

Which Sci-Fi work first showed weapon of galactic-scale mass destruction?

Sounds like space opera to me! E. E. "Doc" Smith's Skylark DuQuesne, 1965:

Dorothy’s face began to pale. “By that analogy you mean destroy the
whole galaxy! How can such a thing be possible? It can’t possibly be
possible!”

He told her how the operation could be performed. That apparatus that
the Barlo women had dredged up out of nowhere had a lot of capabilities
that did not appear on the surface. Blackie DuQuesne had perceived one
set of those possibilities, and he and Blackie had been working on the
hardware. They were calling it Project Rho.

The effects of Project Rho were to destroy two galaxies. One galaxy was destroyed by removing most of its stars:

In Galaxy A, where billions of suns had gone through
the stellar cycle of evolution for billions of years, there was scarcely
a corporal’s guard of primaries left. It was a strange, almost a
frightening sight. For with the loss of the suns the composition of the
galaxy had changed to something never before seen in all the plenum of
universes. Nearly every sun had had planets; nearly every planet
remained behind when its sun was stolen. Now they roamed at
random—uncontrolled, barren, uninhabited—lacking not only the light
and heat of their primaries, but freed from their gravitational reins as
well.

The stars from galaxy A were teleported to the galaxy of the Chlorans, which in turn caused all its stars to explode:

Thus millions
upon millions of Chloran planets were destroyed without any intelligent
entity either giving or receiving warning that an attack was being made....

They died in
uncounted trillions. The greeny-yellow soup that served them for air
boiled away. Their halogenous flesh was charred, baked and desiccated in
the split-second of the passing of the wave front from each exploding
double star, moments before their planets themselves began to seethe and
boil. Many died unaware. Most died fighting. Some died in terrible,
frantic efforts to escape...

But they all died.

Possibility might be a weapon in Edmond Hamilton's novel "The Star Kings." This weapon was the "Disruptor," able to annhiliate vast regions of space itself and hence all matter within it.

In the Star Trek episode "The Alternative Factor", 30 March 1967, A highly unscientific threat to destroy our entire universe plus an alternate one was revealed, destruction on a scale that makes mere galaxy-wide destruction seem infinitesimal:

KIRK: What's going on? This leaping from universe to universe. This wild talk about a murdering creature who destroys civilisations What's the purpose?

SPOCK: Jim, madness has no purpose or reason, but it may have a goal. He must be stopped, held. Destroyed if necessary.

KIRK: I don't follow you.

SPOCK: Two parallel universes project this. One positive, the other negative. Or, more specifically, one matter, the other antimatter.

KIRK: Do you know what you're saying? Matter and antimatter have a tendency to cancel each other out. violently.

SPOCK: Precisely. Under certain conditions, when two identical particles of matter and antimatter meet.

KIRK: Like Lazarus. Identical. Like both Lazarus', only one is matter and the other antimatter. If they meet.

SPOCK: Annihilation, Jim. Total, complete, absolute annihilation.

KIRK: Of everything that exists, everywhere.

And when Kirk meets the sane Lazarus:

KIRK: Antimatter?

LAZARUS: Here, yes.

KIRK: And if identical particles meet

LAZARUS: The end of everything. Civilisation, existence, all gone. I tried to stop him, Captain. That's why I took your dilithium crystals.

Of course "The Alternative Factor" was aired in 1967, after Skylark DuQuesne (1965) and The Star Kings (1947) were published.

=>There is a "curse" that could destroy the entire fictional civilization in a book called "The Magician's Nephew"(1955) by C.S. Lewis.

The Deplorable Word, as used in The Magician's Nephew, by author C. S.
Lewis is a magical curse which ends all life in the fictional world
of Charn except that of the one who speaks it.

=>There was also this 'The Illudium PU-36 Explosive Space Modulator' in the classic Bugs
Bunny short Haredevil Hare in 1948. Marvin the Martian wanted to use it to blow up
Earth because, as he said, "It obstructs my view of Venus". The explosive was in the form of a small red stick that resembled Dynamite that was screwed into a large telescope-like machine.

=>In E. E. Smith's The Skylark of Space series(written between 1915-1921) various planet-killers are used or discussed. Throwing planets and moons out of orbit, incredibly high-yield atomic or copper bombs, near-instantaneous dematerialization of physical objects and the teleporting of close to fifty billion stars in order to wipe out a Galaxy-wide alien civilization are all used.