ZDoom

Gonna plug my own [url=https://jp.itch.io/doom-runtracker]stat tracker mod[/url], also written in ZScript.

https://img.itch.zone/aW1hZ2UvMjA4ODk0LzIwODIzNTQuanBn/original/D%2BuwEy.jpg

You don't have to change engine code for this, scoring is doable mod-side with ZScript. Shameless self-promotion: [url=https://forum.zdoom.org/viewtopic.php?f=105&t=66565]Lazy Points[/url]. Not exactly what you ask for, but it stores high scores between maps and between games, and has a menu to view scores. Maybe it will serve as a starting point for your own thing.

Note that there is a score statistics, though it's something that is only of use with mods that assign scores to monsters and items. All vanilla actors are scoreless.

There's already something to track your achievements.
At the console, set 'savestatistics' to 1 and it will write out your play time and monster/item/secret count when you complete an episode.
It's rather unlikely that this wlll get extended to true highscore maintenance because that's rather tricky with a game that has no concept of scoring in a competitive way.

[quote="bebipbop"]Another quick question. Is GZDoom open source? Like could I just edit this myself and make my own little version with highscores? What languages would I have to learn?[/quote]
yes, yes, C++

Another quick question. Is GZDoom open source? Like could I just edit this myself and make my own little version with highscores? What languages would I have to learn?

Something to keep track of my highest monster kill % per level (same for items and secrets([b]and best time[/b]))

Idk where this would be but I guess thats up to gz. Probably just in the end of level screens or something. I just think it would add a lot of replay value if GZ kept track of your best stats per difficulty/level somewhere just to give you something to play against. Seems easy to implement tbh (but I'm not much of a programmer). Even if it's just a menu tucked away somewhere in the pause menu it'd be cool.