When $3,000 of deferrals are recharacterized as catch-up at 4/30/19 due to the failed ADP test, that also reduces the regular deferrals from 1/1/19 - 4/30/19 that count towards the 402(g) limit by $3,000. The end result is that the participant still gets to defer the full 402(g) limit plus the catch-up limit for the calendar year. To me, that result makes sense because the individual's maximum deferral is not affected by the plan's determination of the catch-up [see 402(g)(1)(C)].
A calendar year plan is a little different because a participant who defers $25,000 in 2019 has used up all of the 2019 catch-up limit before the end of the year. 402(g) triggered catch-ups are not used in the ADP test. Also, if there is a refund due, the full catch-up limit has already been used, so none of the refund can be recharacterized.
With the participant having $6,500 recharacterized as catch-up at 4/30/20 from a failed ADP test, that means all of the participant's deferrals from 5/1/20-12/31/20 are included in the PYE 4/30/21 ADP test. The participant still gets to defer up to $26,000 for calendar year 2020.