Star Trek: Picard established that Starfleet stores its most legendary starships at the Athan Prime Fleet Museum, but it's unclear if the museum is still in operation in Star Trek: Discovery's 32nd century. The Starfleet Museum was first seen in Star Trek: Enterprise's series finale, "These Are The Voyages…" when the refitted Enterprise NX-01 was added to the collection. The museum and its collection have presumably had several upgrades since then, allowing it to exist long into Star Trek's future.
When the USS Discovery arrived in the 32nd century, they found Starfleet and the Federation in a weakened state following the devastating events of The Burn – a subspace shockwave that destroyed countless Federation starships. The shockwave destabilized the dilithium used to regulate anti-matter containment during warp travel, causing all active warp reactors to detonate. This left Starfleet's armada severely depleted, but it's unclear if The Burn affected the Starfleet Museum and its impressive collection of antique starships.
