Gaming

You might want to look specifically at rogue 'lites' which tend to have some form of upgrade system outside of the main gameplay loop. In Hades for example, you pick up certain items during a run which you can use to upgrade your character after you die. Other ones that spring to mind are Dead Cells, Slay the Spire, Monster Train and Rogue Legacy. All of these have generally quite short sessions and each run lets you improve your character for subsequent runs.

I want to point out the obvious choice by recommending Minecraft. It is very easy to proficient, acquiring in game materials is all you do. Play sessions can be as long as you want since it is a open sandbox and you can add as much depth as you want via mods.

Might’ve meant “material” progress, like “tangible” or progress that’s real and meaningful? “Materialistic” I think usually just means thinking about things you own rather than the quality of your life and relationships? Though saying it out now, I guess that works kind of… But I’ve only ever heard “materialistic” referring to people who only care about what someone owns rather than being a good person; never about video games or the kind of progress I think you’re wanting.

Anyway, lots of good suggestions here. I can’t add anything that meets all your qualifications; but if you are willing to dramatically break your install size requirement, I’ve been having a lot of fun lately with the Forza Horizon games (4 and 5) which are open-world racing/challenge games; but literally everything you do contributes to experience points and money you can use to upgrade and purchase new cars, and there are a lot of challenges which aren’t just races, there’s speed trials (how fast can you hit this one stretch of road), trick trials (how many jumps can you pull if in a minute) and so on.

But the install is like 65GB for FH4, and 150+GB for FH5… hundreds of high detail cars and massive open worlds, I guess… :(

Outer Wilds. By it's very nature, the game splits itself into 20 minute blocks.

You don't make 'materialistic progress', but you'll almost always make progress in the game; the progress you make is finding out new information. Yes, it starts over every time, but you aren't losing progress. It's also just, in general, an excellent game.

Hades or dead cells - both are fantastic roguelites that you can pretty much pause at any time and have loads of replayability

Super auto pets!

Vampire Surviver spawned a new genre of games that are great single session games. There are a lot of variations, but the core loop of vampire survivors is similar to a rouge-like, but focuses on making each run fun and rewarding. You generally get points of some sort for a run, which you invest into a skill tree or stat points, and your next run is better as a result. Even most rouge-lites try not to give you a huge advantage with your unlocks, but Vampire Survivor and it's ilk really focus on that. As a result, the repetition isn't as brutal, and death doesn't feel like a punishment.

"I have looked into the genre of roguelikes, however the basic premise of these games are that they start all over again from each session, which is what I am trying to avoid."

...Except this isn't true of what we'd traditionally call rogue-lites, which is really most roguelikes these days. The vast, vast majority have a lot of meta progression systems to the point where people actually expect it these days.