Having a task list is definitely a positive (I know it can be tedious to do so it's absolutely appreciated). But it shouldn't be absolutely necessary for every single step to help you figure out (it already isn't, but the less often you feel you
have to look up how to progress the better).
I can't really give a good tip there (without playing through it again) except double-check the writing of the scenes and how much indication there is on what to do next. If the scene ends with "phew, I'm done. Time to catch some Zs" you know you gotta go to bed. That sorta thing is good.
If you want to go fancier then minimap with character locations could be a good, somewhat more organic hint. You know Fae is in her lab, it shows on the map, presumably you gotta go there if you got something to do with her ...
The idea is fine, I think, it's just the needless clicking about without much of a motivation. I actually really appreciate any level of dynamic background (ie you clean stuff, it actually looks cleaner - nice). But (for example) I'm not a big fan of anything that feels like extra clicks, and given that your only interaction option with the "dirt" is cleaning it anyway to click on a spot, click clean, have a little comment, click on the next one ... it's just slightly tedious. No big crime or anything, but given that there isn't much else yet it's a small problem.
A stream-lined example could be something like entering a room, if cleaning quest is active, "well, gotta clean now", then your cursor changes to a rag (or doesn't, or maybe you first got to get the cleaning supplies, or...) and you just need to click all the spots, done. Same thing, slightly less tedious, I think. Depends on how fancy you wanna get ^^;
I've played hundreds of adventure games and what I've learned is that ... designing good puzzles is very hard
(aside: also not too long Dave Gilbert of Wadjet Eye fame in his Discord talked about his puzzle designs a bit; and how they need to be balanced against the narrative. You don't want to have a huge obstacle every time you want to progress the plot when the game is meant to be more a narrative experience - essentially you gotta decide where on the "walking simulator (VN)" <-> "hardcore puzzle game" spectrum you want to be...).
But yeah, absolutely honestly, the most mystifying aspect in designing a good p&c to me has always been the puzzles. I don't mean the sorta puzzles you always see; variously adapted minigames (for example Tower of Hanoi), math puzzles (for example having 3 differently aged people and having to figure out how old the forth is) or some of the classic switch puzzles (ie switch A turns on switch B but turns off switch C, switch B turns off switch A and switch C, switch C ... figure out how to get all switches turned on). Those types of puzzles you can adapt to your narrative and players can figure them out according to their rules.
But more the good inventory puzzles that are neither so out there you got no clue on what to do nor so easy it feels like a hassle the developers just introduced to keep you busy ^^;
That being said I'd assume that good design according in a game like this one wouldn't be going too hardcore with puzzles, but just rather basic stuff that makes the experience a bit more interactive, that allows the players to explore different locations with a bit more drive ("I'm doing this now so I can get the thing that I need to solve the problem so I get to see more boobs" ... or smth).
In that regard of course anything can be a puzzle. A door doesn't properly open. Find some oil to oil the hinges. The oil can is empty. Is there anything you can find that'll replicate the effect? Squeeze it into the oil can. Oil the hinges. Door opens.
Fae wants coffee. Go make coffee. The coffee maker needs a new filter. Break into Fae's room and repurpose some fancy panties for coffee filtering purposes.
You gotta clean the bath. There's no mop. Find something that'll work as a handle and a, uh, mop head? Stick it together.
Or maybe mix some bleach out of some stuff because there's no cleaning supplies. No idea, make soap?
Find fuses for things, or pass codes, or scifithingamabobs that doathingthatsnecessary.
Maybe first time navigation needs some sort of "lining up a route" puzzle;maybe first time exploring a planet (or drudging through the snowstorm) has you go through some room labyrinth (ie you gotta go north-north-south-east-south-north or whatever and if you mess up you gotta try again or something).
... basically I think play up the whole "this is an old rust bucket of a ship that's got all sorts of problems so we gotta fix stuff all the time" and add some sort of interactivity at major points.
But like I said. I'm the opposite of confident in my puzzle designing ideas; those are just "seen elsewhere" things. Hardly interestin or creative. ^^;
I suppose technically you could look at games like JULIA Among the Stars, Primordia, Shardlight etc.; just the walkthroughs and see what the game requires the player to do to progress for some inspiration. But dunno how helpful that is.
Also, of course, I understand any of this would be all sorts of work (some more, some less); you guys gotta judge what's doable and what isn't. I
got the vague feeling that ie if you give players the choice between "hey, we can add more interactivity to the sex scenes, or add more puzzles, which do you want..." ... well, that answer is going to be one answer only for most
Anyway, hope this helps somehow a little ^^