[MangaArtist18]

SO.

Lemme see if I've got this figured out, from all the info I've dug up.

Basketball player becomes Another Build.

New timeline where Katsuragi never became Sento, and Sento never became Build, and thus, Cross-Z doesn't exist. So now the Another Build is, by all definitions of the name, Build.
But the relationship between Katsuragi and Sento isn't changed? They're still good pals (over Linkz, but same thing).

Sougo and Geiz attack Another Build, not really killing him. This doesn't exactly fix the timeline, but "jogs" Katsuragi's and Banjo's memories.

Cut back to 2018, and Katsuragi and Banjo have their Rider gear. This creates a paradox where two Build timelines cannot coexist in the same space (the "glitches" seen during the fight).

Sougo uses Build's power (the Ridewatch) to defeat Another Build. This fixes the timeline, so Sento and Banjo have their powers again. This also likely erases the Build/Cross-z Ridewatch.

Sougo and Geiz then return the basketball player to 2017. Sougo runs up to Katsuragi and Banjo and gives them blank Ridewatches, ensuring that Geiz and Zi-O can still use the Build (and Cross-z) Ridewatch in the future.