Is there a reason to complete additional research tasks after a Pokédex entry is completed?
A Pokémon's entry in the Pokédex is considered complete once you reach Research Level 10. However, there are usually several unfinished tasks left after a Pokemon's research is "complete".
Is there a reason to keep completing a Pokémon's research tasks after its Pokédex entry has been completed?
Yes, there are multiple benefits to completing all research tasks.
By perfecting the research, you get a huge boost to encounter a shiny for that species. The shiny rate becomes a base 1/1024( https://www.serebii.net/legendsarceus/shinypokemon.shtml ) chance for standard encounters rather than 1/4096, along with other factors to further increase it
As https://gaming.stackexchange.com/users/51234/joe stated in their https://gaming.stackexchange.com/a/395817/124566 , performing the tasks to perfect a Pokémon's research will continue to grant research points to achieve 10 Stars in the Galaxy Team Rank. https://gaming.stackexchange.com/users/253677/brade also mentioned in a comment that simply achieving rank 10 for each Pokémon was not enough to reach 10 stars, so continuing (albeit not necessarily perfecting) these tasks is required to reach max rank.
As https://gaming.stackexchange.com/users/87579/pinckerman stated in their https://gaming.stackexchange.com/a/395819/124566 , the Pokéball icon that appears next to the Pokémon in the Pokédex turns to a shiny Pokéball.