Overview
========
Staples (aided by a counting circle)
Sudoku (aided by a counting cirlce)
Counting circles redux

Staples
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The only available staples are 1-[89]-[89]-7, 2-[19]-[19]-8 and 3-[12]-[12]-9
Therefore, they always contain a 1 and a 9.
Because they pair up in rows, columns and boxes, r[45]c5 is a [19] pair.
=> The counting circle r4c5 is a 1.
This sends a cascade of [1289] (and occasional 3 or 7) around the grid until it's uniquely:
2198, 7891, 1987, 8912, 8912, 3219, [39][12][12][39] clockwise and clockwise.

Sudoku
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The counting circle make r5c1 the 8th 1, resolving the [12] on the final staple.
r1c8 is the 5th 2, and the final 3 drop in immediately afterwards
r6c5 is the 6th 8, and with the aid of the counting circle r5c3 and r8c2 follow.
The final two 9s likewise drop in immediately.

Counting circles
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We had 12, but one is 1, so we need 11 more. 7's not satisfiable, and 2's all spent, so it's 6+5
r3c4 has to be 6 no matter which way the other 10 cells split - colour the five [56] pairs.

Sudoku again
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You can now colour [47] pairs all over the place, placing some 3s in r9c8, r4c7, r2c9, r5c4.
r6c6 becomes a 4, and the [47]s unwind.
In so doing you'll squeeze a [56] into r3c7, which cascades all over the grid
And you're done.

Proof of uniqueness:
https://sigh.github.io/Interactive-Sudoku-Solver/?q=.Lockout%7E4%7ER2C3%7ER1C3%7ER1C4%7ER2C4.Lockout%7E4%7ER1C6%7ER1C7%7ER2C7%7ER2C6.Lockout%7E4%7ER3C9%7ER4C9%7ER4C8%7ER3C8.Lockout%7E4%7ER7C9%7ER7C8%7ER6C8%7ER6C9.Lockout%7E4%7ER9C6%7ER8C6%7ER8C7%7ER9C7.Lockout%7E4%7ER8C3%7ER8C4%7ER9C4%7ER9C3.Lockout%7E4%7ER6C1%7ER7C1%7ER7C2%7ER6C2.Modular%7E3%7ER2C3%7ER1C3%7ER1C4%7ER2C4.Modular%7E3%7ER1C6%7ER1C7%7ER2C7%7ER2C6.Modular%7E3%7ER3C9%7ER4C9%7ER4C8%7ER3C8.Modular%7E3%7ER7C9%7ER7C8%7ER6C8%7ER6C9.Modular%7E3%7ER9C6%7ER8C6%7ER8C7%7ER9C7.Modular%7E3%7ER8C3%7ER8C4%7ER9C4%7ER9C3.Modular%7E3%7ER6C1%7ER7C1%7ER7C2%7ER6C2.CountingCircles%7ER4C5%7ER1C2%7ER3C4%7ER1C9%7ER5C8%7ER6C7%7ER8C8%7ER9C9%7ER8C1%7ER7C3%7ER6C3%7ER5C2

https://sudoku.coach/en/s/DHmv