Although Pokémon is a role-playing game, it has never really stuck to the usual gameplay tropes associated with the genre. In particular, the series suffers somewhat due to the lack of side content outside of completing the Pokédex, but that doesn't mean there isn't any side content, it is just usually not openly given to the player so freely.
From Gold & Silver onwards, Game Freak has slowly but surely started to embrace side quests in Pokémon games, with Sword & Shield having a great deal of side content that is fairly easy to find, particularly in The Isle of Armor and The Crown Tundra DLC. However, there are many side quests from earlier games that many players can miss due to how hidden they are.
10 Pokemon Eggs: HeartGold & SoulSilver
The generation two games introduced the concept of Pokémon breeding and Pokémon eggs, with the Togepi egg being a minor plot point for the early sections of the story. HeartGold & SoulSilver expanded on the Togepi story, but also added a handful of new Pokémon eggs that can be found in the Violet City Pokémon Center. After talking to Primo, the man in the top right-hand corner of the center, he will ask the player a series of questions that need to be answered. The answers are different depending on which version of the game is being played as well as the player's Trainer ID, but with some Googling, players can find themselves a Wooper, Mareep, and Slugma egg before defeating the first gym in Johto.
9 The Ditto 5: Ultra Sun & Ultra Moon
One of the more recent side quests is a mission given to the player by a police officer just outside of Diglett Tunnel. The quest can be triggered by going inside the Police Station and talking to the officer at the rear of the building, who is actually a Ditto, and defeating or catching it. The officer at the front desk will then give the player a mission to find the other four Ditto hidden in Konikoni City, giving the player a new hint on the location of the next one once the previous one has been dealt with. These Ditto are worth catching as they are decent options for breeding with other Pokémon.
8 The Lost Minccino: Sword & Shield
This side quest is relatively short if players know where the lost Minccino actually is, otherwise it can send players searching all around the city looking for this mouse Pokémon. After talking to one of the boys near the west exit of Motostoke, in front of the warehouse buildings with a Lapras painted on them, he will ask the player to find his lost Pokémon.
To find the Minccino, simply head east, back towards the Pokémon Gym, and interact with the water fountain on the left-hand side. The Minccino should make the "mworp" sound which can then be lured out by whistling at it. Returning to the boy will grant the player a Throat Spray item.
7 Love Letter: Sword & Shield
In Hammerlocke, on the second level just above the train station, there is a castle with a little girl standing in front of it who asks the player to deliver a love letter for her. The man, Frank, lives in Ballonlea, in the first house on the left accompanied by two children. He says that the girl, Paula, was a childhood friend of his who became very ill and he hasn't seen her since, though she very clearly died of her illness. Frank will give the player a Choice Scarf, but if players go back to where Paula was standing, they will find a Reaper Cloth in her place, the evolution item for Dusknoir.
6 Game Freak Staff Member Battles: Various
Game Freak staff members have been in Pokémon games since Red & Blue, but they weren't able to be battled until a few generations later. In Sword & Shield, a Game Freak staff member can be found in Circhester inside the hotel. Go up to the second floor and enter the first door on the left, where there will be a Police Officer wearing a Dynamax Band. Talking to this NPC after defeating the Pokémon League will trigger a double battle with a very strong trainer. His team consists of Cursola, Graploct, Coalossal, Stonjourner, Dragapult, and a Snorlax that he will Dynamax.
5 Message In A Bottle: Ultra Sun & Ultra Moon
In one of the houses in Iki Town, players will find an old woman who talks to the player about her long lost brother, who would collect sand with her when they were children. Once players reach Kala'e Bay, they can find a shiny spot on the ground that, when interacted with, will present the player with a message in a bottle from a man addressed to his sister. Taking this message back to the old woman will put her mind and ease and she will reward the player with a Stardust.
4 Post-Game Evolution Stones: HeartGold & SoulSilver
The post-game content, while a nice addition that has yet to be replicated in any game other than Gold & Silver and its remakes, was fairly short in the original generation two games. HeartGold & SoulSilver sought to rectify that by adding a huge amount of things to do once players have defeated the Elite Four. One much smaller addition was Bill's grandfather, who takes up residence in Bill's old house.
This old man can be talked to daily and will request that players show him a specific Pokémon in exchange for an evolution stone. He doesn't say openly which Pokémon he wants to see, however, so players will have to guess which Pokémon he is referring to when he asks to see one.
3 Extreme Speed Dratini: Crystal and HeartGold & SoulSilver
The trainer quiz that allowed players to obtain the Rising Badge from Clair was present in HeartGold & SoulSilver, but it wasn't introduced in generation two until Pokémon Crystal. If the player returns to the old man after taking his quiz, he will grant them a Dratini, but if they gave him specific answers to his questions, the ones that are obviously the best choice, he will still grant the player a Dratini, but it will know Extreme Speed. This was one of the only ways to get Extreme Speed on a Dragonite before it became an egg move in later generations and is worth getting in any playthrough.
2 Minding Slowpoke: Let's Go Pikachu & Eevee
This is a very simple and very boring side quest in Let's Go Pikachu & Eevee, but it is also very easy to miss. In Pewter City, just above Brock's gym, there is a woman with a Slowpoke who asks the player to mind it for her while she runs an errand. After staring intently at Slowpoke's rear end for a few moments, she will return from her errand and grant the player a Big Pearl. While it is easily one of the dumbest side quests in the game, getting an item that can be sold for such a high amount of money early on is very helpful in a game that requires the player to buy a ton of Poké Balls.
1 Spiritomb: Sword & Shield
The most recent DLC, The Crown Tundra, has many hidden Pokémon that can be found or caught in the game, but the most innocuous is how players can get a hold of Spiritomb. From the Dyna Tree, if players head out into the Wild Area towards the dead-end corner, they will find a tombstone that reads "Spread my voice." In a reference to how players obtained Spritomb in Diamond & Pearl, players need to interact with multiple people in the overworld while connected online. After interacting with enough people, there will be a Spiritomb standing in front of the tombstone.