With power chords you had root and fifth. Now add the third to get a full major or minor chord. In fourths tuning, each quality has one shape that works everywhere. Learn two shapes, play every major and minor chord.
The Major Barre Shape
This 4-string voicing spans strings E-A-D-G. The intervals from the root: major 3rd on the next string (one fret back), fifth two strings up (three frets back), octave three strings up (also three frets back). The shape is compact and the same everywhere.
Notice G major: when the shape falls near the nut, some notes land on open strings. The shape is still the same - the open strings just happen to be the right notes.
The Minor Barre Shape
The only difference from major: the 3rd drops by one fret (major 3rd becomes minor 3rd). That is it. One fret changes the entire mood of the chord.
Compare Side by Side
Here is A major next to A minor. The only fret that changes is on the A string: fret 4 (major 3rd, C#) versus fret 3 (minor 3rd, C). Train your ear to hear this single-fret difference.
Move to Other String Groups
The shapes also work rooted on the A string (spanning A-D-G-C) or the D string (spanning D-G-C-F). Same shape, different register.
Practice
Strum A major four times, then A minor four times at 70 BPM. Repeat with D, G, and C. Focus on keeping the barre firm and every note ringing clearly. Once comfortable, try a I-vi-IV-V progression: C major, A minor, F major, G major - all using the same shape slid to different positions.