feat(random): group the random pickers into a random module and add /gachabeta

/random, /wheelofnames, and /gacha move from misc into a new random module
with unchanged command names, so usage stats carry over. The new unlisted
/gachabeta takes the same input as /gacha and renders the toon-shaded beta
wish from /api/gachabeta on the same service, with the same text fallback.

docs/deploy-coolify-selfhosted.md

@@ -93,6 +93,11 @@ option is equally likely, as with `/random`; the rarity only sets what the
 animation and reply show. Options are 5★ by default; prefix `4*` or `3*` to
 lower one, e.g. `/gacha Pizza, 4* Pho, 3* Rice`.
 
+The unlisted `/gachabeta` takes the same input and renders the 8-second beta
+style from `.../api/gachabeta` on the same service (a toon-shaded sky, a comet
+bursting through a cloud, and an `S`/`SS`/`SSS` rank for 3★/4★/5★), with the
+same text fallback.
+
 ## 1. MongoDB Atlas (M0)
 
 1. Create a free **M0** cluster (512 MB — ample for the tiny paper-trading KV).