You attempted to explain away the lack/delay of game updates on Gog by labeling updates that have been published in the game's default branch [Steam] as 'beta'.
Expeditions: Rome doesn't have a public beta branch on Steam BTW
I tell you what the devs tell me, they didn't see it as a official patch, they public the official patchs in the update tab, just like it happen with this latest one. As soon as they release a new officil patch they bring it to GOG at the same time.
Half of all game updates did not appear in the "update tab" [Steam], and yet
all game updates on Steam also arrived on Gog on the same day or the next, except for two: Hotfix 1.4 ("official", ~4.5 months later) and Patch 1.4.1 (~3.5 months later).
Expeditions: Rome [Steam] > View update history Patches [SteamDB]
"Official" patches (in update tab/"certified") since full game release January 20, 2022; all but one (Hotfix 1.4) published on Gog same day/+1d as on Steam:
Jan 27 [Regular Update] Hotfix - v1.1.4
Mar 29 [Major Update] Patch 1.3 Apr 13 [Small Update / Patch Notes] Hotfix 1.4
Aug 30 [Major Update] The Controller Patch Version 1.5
Patches not in update tab, since full game release January 20, 2022; all but one (Patch 1.4.1) published on Gog same day as on Steam:
Jan 24 [News] v1.1.3 - Patch Notes
Feb 09 [News] The "little" Patch - V1.2.0
Feb 17 [News] 1.2.1
Apr 12 [News] Expeditions: Rome Gets Gladiator-DLC "Death or Glory" May 16 [News] Good news everyone! Patch 1.4.1 is now out
I wonder if the little Gog-exclusive bug BUG: missing unlocked customizations
has been fixed.