Two things regarding Y1 green rain, especially now that gift-giving gets blocked under the "resulting dialogues break the mood" logic —
Help Wanted orders that show up the day before the rain (while the poor weatherman is losing his mind) can be fulfilled during it; my current game had a request for hot peppers come up the day before they ripened... which was indeed Green Rain Day. Fulfilling the order got the standard "oh hey thanks!!
"-style response, from a character who was freaking out in daily-chat dialogue.
Also: if you ask Robin to upgrade your house, on the forecast day, she shows up for the first day in the green rain with her standard working-on-your-house dialogue; the second day has her "I hope he's happy with his samples!" grumpy-at-Demetrius line.
I am admittedly playing on a very heavily modded game right now (in part because I keep expecting it to completely break my not-very-RAM-powered laptop), and the help-wanted order went to an SVE character — but if the bulletin board's functionality is blocked by the base game, I can't imagine the mod author would have specifically overridden it (and I'm not using any mods that are meant to override or alter the behavior of the errand board or tasks) — hence reporting it here instead of on the mod page.
Steam (but launched through SMAPI directly/Steam not open), everything up-to-date as far as I can tell, Windows 11 Home, in English.