Here's my 2 cents. A lot of people have mentioned what to add to the game, but not what to keep. But I'll also touch on what I think could be worth adding. I have been playing RPG's my entire life so please allow me to convey my culmulative knowledge into ideas for SaS2.
Currently what makes SaS so good are these underlying facts: it's a single player experience where the player can customise their hero and grow at their own pace. The training room provides for challenging and entertaining experience, where the 'Mission' for each minigame keeps the player interested while the 'combo' keeps the player aiming higher and higher, but also serves as a benchmark for how well they've done. The player can then experience the fruits of the labour through the arena and see how much the training has paid off, this in turn leads to the reward of being able to afford armour, weapons and upgrades, to further enhance their training. All together, it's a very satisfying experience and that's why these basic features should not be changed or removed, but rather, expanded. Here's how I think it would be best to expand these features without removing the satisfying element.
Training room:
Missions and combos should definitely stay as they provide immediate incentive for training. The clovers should also be a random occurrence during training but we'll touch on that later. Missions are short goals which are, for the most part, easy to reach and prevents the player from getting bored too fast. On top of this, rewarding, as it provides exp. Providing more diverse goals each time will only delay how long it takes for the player to lose interest, which is exactly what we want. Combos on the other hand are fine how they are, increasing exp and providing that "I must do better" addictive factor. The only problem I see with it is that it stops influencing exp after a relatively short period. Instead, it would be better to have an exp curve in place such as this. I can't quite figure a formula for the curve, but that said, it might just be better to have a manual curve (e.g. If 0<combo<10 Then (exp) += base_exp + xp_curve[0]) Or something like that. The combo would also be perfect on a leaderboard, as it allows players to indirectly compete against each other which is just another satisfying element to the game.
Arena:
Now as for the arena, it provides a good means of making money and to progress through the game. It can get repetitive, so it may be better to keep it how it is, lower the money rewards and have it treated as a benchmark for how strong your character is. Granting Titles to the player for getting to certain points in the arena could substitute for the decreased money rewards, or perhaps trophies to put in your house. The actual progression of the game should be done through dungeons and exploration which follows some sort of story line, as it would be nowhere near as repetitive as the arena. The one limitation with the storyline is the player loses incentive to continue after the story is complete, so it's very important to make the story lengthy by progressing with the players level, satisfying through rewards of exp, money, artefacts, and most importantly to have the player wanting to know what happens next. Characters are very important in this aspect. I won't go into detail here because I myself am not good at story or character design. All I can tell you is that character relationships are very important, especially in keeping the player engaged and driving the story.
Upgrades:
As for allowing the player to upgrade their house and training room, these are fantastic features. What would perhaps make it even better is providing different means of training as the training room is upgraded. Currently the exp bonus is great and should not be removed, but perhaps the player could unlock training minigames that train two stats at once (at a slightly decreased rate of course, e.g. obsticle course trains 0.7xAgility and 0.5xStrength while sparing would train 1xDefense). This would allow the player to specialise in whichever class they choose through more diverse minigames. Upgrading your house is very nice as it provides money/exp bonus as well as a completeness factor. Two things I'd suggest: each part of the house should either contribute to the money or exp bonus, allowing the player to chose which they'd rather invest in. Last thing is that the house didn't look visually appealing to begin with. Perhaps starting with a thatch roof and upgrading to wood, and then to tiles would be better than going from no roof to roof. Same goes for parts such as windows and doors.
Classes:
When it comes to classes, let me stress something. DO NOT lock the player into a certain class by making them chose in the beginning. It is so much better to provide a skill tree, allowing the player to choose the path/paths they'd rather take. Each path speciallising into different play styles and classes. This gives the player the opportunity to specialise into their very own playstyle. Choosing their own paths and playing how they want to play. This is probably the most important part to a compelling rpg experience. With this system and the ability for the player to advance at their own pace, it would make for a very satisfying experience. Currently there is nothing wrong with the stats in the game, each are very clear and have their own unique purpose, but it may be better to rename the stats to Strength, Dexterity, Defense, Agility and Critical. It may just be personal prefference here so take the rename idea with a grain of salt.
Equipment:
Equipment may be a little tricky as it's hard to find the right balance of stats depending on what kind of combat there is. My suggestions for this is having light armour which focuses on Dexterity and Agility but provides little Defense and heavy armour which focuses on Defense and Health but provides little to no Dexterity or Agility. This can obviously be expanded on but that all comes down to the combat system and how equipment would influence playstyles. And then theres the decision to either have equipment in the form of items or upgrades in the shop. Personally I think it would be better to have them as upgrades in the shop, just like how it was in the first game, as this doesn't burden the player with an inventory system. Currently the game is very streamlined and an inventory system would just make things needlessly complex while forcing the player to choose between items gear which can just be annoying at times.
Secrets:
A very nice feature of the game is the lost children. It was fun searching for them, though a little frustrating when theres a few left, but would definitely be worth doing something similar again. Perhaps adding some sort of reward for finding all the children would make it even better. As for the other little easter eggs, I'm sure you plan on putting them in your next game so I don't think I'd need to touch up on this.
Museum:
The museum is perfect the way it is. Providing a passive income and a lore friendly excuse to go with it is amazing. I urge you to keep this feature. But perhaps upgrading the asthetics could do it some good. As for the clovers, they're a nice little bonus when progressing through the game but maybe a clover shop would be better, like trading more clovers at once can give bigger rewards or something like that. Maybe you could change the Critical stat to Luck and have it influence critical hit and the ability to find clovers.
Please take into consideration these ideas as I only wish for SaS2 to be an even more amazing game. Thank you for reading.