Thanks so much, y’all! Sounds like The Black Hack (2e) and OSE(A) come pretty highly recommended. How “fiddly” is OSE? I gave the SRD a look, and I find the presentation quite approachable, but I don’t love how bonuses from ability scores vary from score to score, or certain tasks like opening stuck doors being resolved by an X-in-six roll while others are percentile based and others are a d20 roll, etc. But maybe it feels smoother in actual play than it looks on paper?
B/X-OSE stat modifiers go from -3 to +3 and do not generally apply to skill check type mechanics. 13-15 = +1, 16-17 = +2, 18 = +3. Everybody has ability scores from 3-18 with no ASIs. This means roll 3d6 in order is much more feasible and the stats make less of an impact on character effectiveness. Str is for melee attack and damage, int is for languages, dex is for AC and ranged, con is for hp, and charisma is for reaction adjustment. It is easy to keep track of in practice, only attacks and melee damage modifiers get actively applied in most situations. HP, AC, and languages are applied once then used as the baseline so do not need to be considered again.
For the different types of ability checks there are basically three systems.
Most things are x out of 6. Searching for secret doors. Searching for traps. Listening. Opening stuck doors, etc. Quick and easy.
Thief skills are narrowly defined class specific powers and use percentiles that start off with only tiny chances of success. I have always hated them and prefer Necrotic Gnome's (the company behind OSE)
B/X Rogue for an alt thief class.
In B/X-BECMI-RC roll under an attribute on a d20 was a later skill development system, mostly from the Gazetteer series, that also worked for ad hoc checks. Simple and easy, but places a huge emphasis on individual character ability scores.
Generally it is a DM call on what mechanics to use for non-combat stuff, including no rolls and adjudicating off of player descriptions of what they are doing (player skill) or just adjudicating what happens.
In play it is generally quick and smooth. Either a player calls out a defined thief skill and tells the DM their percentage of success, or the DM calls out a d6 roll or an ability score check.