Villagers do not work in rain. However, fishermen should work in rain because rain is better for fishing and rain increases fishing rates for players. Moreover, in the villager_v2.json entity file there is a separate set of scheduling groups and events for fishermen. However, the fishermen groups are identical to the general villager groups, so this looks like a mistake. My guess is that “can_work_in_rain”: false should be “can_work_in_rain”: true within "work_schedule_fisher".
Steps to reproduce
Set time to day.
Set weather to rain.
Place a bed and barrel.
Spawn a villager.
Expected result
Fisherman works.
Actual result
Fisherman does not work.
It would also add dynamic realism to have the fisherman go to work before sunrise and inspect water blocks like librarians inspect bookshelves.
UPDATE: Having them path to water as a secondary behavior during the work day is partially viable using the right parameters. Unfortunately though, minecraft:behavior.move_to_water struggles to locate 1-block-deep water: MCPE-122278.