Others note that you should learn chords in a musical context. That's true, but I think the crux of your question is getting over the feeling of bewilderment over too many chords. I think you want to "woodshed" on keyboard chord shapes to breakthrough that problem.
Time to set constraints and look for patterns...
First, be mindful of chord symbol redundancies.
add6 chords for example. C6 is an inverted Am7 and Cm6 is an inverted Am7b5. All those symbols may obscure the fact there is a small set of basic chord types.
Start with a reasonable set of basic chords:
IMO skip augmented. It's certainly rare. And, there is some theoretical debate if it's a true tonal chord.
- Major seventh
- Minor seventh
- Dominant seventh
- Diminished seventh
- Half-diminished seventh
There are other seventh chord types, but those above are the commonest.
Find patterns and reduce.
There are six keyboard shapes for the major triads and another six for the minor triads. The roots of those major triads are
F ascending to
Bb, and the minor roots are from
Bb ascending to
Eb. Chords on the other roots are duplicates in shape. So, the "shape" of the
C major triad (all white keys) is the same for
F major and
G major. Skip the duplicates in the beginning. When you get comfortable with the reduced set advance to the whole set of 12 chromatic roots.
Every major seventh and dominant seventh chord contains the set of major triads, and likewise for the minor sevenths and minor triads. That means 3/5 of the set of seventh chords can be conceived of as the triads you already know with the addition of only two more intervals a major seventh and a minor seventh above the chord root.
If memory servers, there are 8 shapes each for the major, minor, and dominant seventh chords. So there is some reduction to exploit with that too.
Regarding my idea of reduce and skip, you could do it literally, and it might be helpful at the very beginning to save time and hand fatigue, but it's better to think of it as mental reduction. Be aware when practicing that Cm, Fm, and Gm are the same shape and so on. It's not exactly 12 totally different minor triads, it's 6 with duplication.
Half-diminished chords are the same as a minor seventh chord with the chord fifth lowered. Yes, it's a different chord. Yes, it has a different harmonic function in a key, but in terms of keyboard fingering technique it's only a half-step alteration of the minor seventh.
Full diminished seventh chords. When inversions are accounted for, there are only three kinds of diminished seventh chords! So,
Bb diminished seventh is the same group of notes as
D diminished seventh. They are inversion of the same chord.
If you total all of those shape types - and exclude the duplicated triads - you get about 35 unique shapes. The basic triads and seventh chords are not endless and you can manage them when you constrain and reduce.
But, how to handle all the inversions?!
The first part is mental. Realize inverted chords are all alterations of the basic root position chord. Don't let that mentally psyche you out as 4 times more stuff to memorize. Think of it as modifications of what you already know.
The second part is the actual practicing of the inversions.
First, play the root position chords until they become familiar.
Next, incorporate the inversion into repetitions of practice drills. Instead of playing pattern X three or four times, move through the various inversions for each repetition.
When practicing these chord forms move through the root chromatically - ascending and descending - rather than the circle of fifth. Yes, a circle of fifth pattern will better reflect harmonic function, but I think you are trying to deal with the keyboard fingering challenge. When fingering is the main concern, I think the chromatic progression is more beneficial. In the beginning it will be challenging. Your fingers will get all mixed up. But when you finally overcome that challenge your command of the keyboard and control of your hands will be greatly improved.
Another practice pattern that seems to help me is repeating pattern x over three octaves without loosing a steady beat. Don't keep repeating stuff with your hands locked into a position. If you're having finger independence trouble, that's another story, and you may need to stay in a position for a while. Otherwise, don't get stuck in one place. Move up and down to the next octave for each repeat. If it's difficult, slow down the tempo. I have found repetitions in this manner are a great exercise of keyboard harmony.
Consult some classical piano methods for ideas of the actual patterns to practice. But, just hitting the 'block chords' is a simple and quick way to get started now.
If you devote about 30 minutes to an hour each day concentrated practice for 6 months, I'm sure you will overcome this problem!
...before I leave this planet...
Because we are determined in our goal, I thought I should add something about the harmony foundations of jazz and classical styles. After getting the fingerings under control these are the important harmonic patterns.
All the above patterns should be played in all major and minor keys.