Non-consecutive (NC), killer-X. The cages are maximum repeat so: XYZ-XYZ or TU-U.
After step 3, most statements about NC have been omitted.
Prelims
a) 22(3) cage at R3C3 = {499/688/877}, no 1,2,3,5
b) 22(6) double cage at R3C4 = {137137/146146} (cannot be {128128/236236/245245} because of double-row NC), no 2,5,8,9
c) 26(6) double cage at R4C3 = {139139/148148/157157/247247} (cannot be {238238/256256/346346} because of double-row NC), no 6
d) 28(6) double cage at R4C6 = {149149/158158/248248/257257} (cannot be {167167/239239/347347/356356} because of double-row NC), no 3,6
e) The blank double cage at R6C4 cannot contain consecutive numbers because of double-row NC
1a. 22(6) double cage at R3C4 = {137137/146146}, 1 locked for R34 + N25
1b. Killer pair 1,2 in 22(6) double cage at R4C3 and 26(6) double cage at R4C6, locked for N5 -> no 1,2 in R456C5
1c. 28(6) double cage at R4C6 = {158158/248248/257257} (cannot be {149149} which clashes with 26(6) double cage at R4C3), no 9
1d. No 1 in R6C456 -> no 1 in blank double cage at R6C4
2a. 6 in N5 only in R456C5, locked for C5
2b. R456C4 = 13, R456C6 = 14 -> R456C5 = 18 = {369/468/567}
2c. R456C5 = {369} (cannot be {468} which clashes with 22(6) double cage at R3C4 = {146146}, cannot be {567} because of NC), locked for C5 and N5
2d. No 3,9 in R456C4 -> no 3,9 in 26(6) double cage at R4C3
2e. 28(6) double cage at R4C6 = {158158/248248/257257}, R4C6 = {147} -> no 4,7 in R56C6
3a. 26(6) double cage at R4C3 = {157157/247247} (cannot be {148148} which clashes with 22(3) cage at R3C3), no 8, 7 locked for C34 + N45
3b. 28(6) double cage at R4C6 = {158158/248248}, no 7, 8 locked for C67 + N6
3c. 22(3) cage at R3C3 = {499/688} -> R4C2 + R5C1 must contain at least one of 8,9 -> no 8,9 in R4C1 + R5C2 (NC)
3d. R6C12 must contain one of 8,9, R6C56 must contain one of 8,9 (R5C56 cannot be [98] because of NC) -> killer pair 8,9 in R6C12 and R6C56, locked for R6
4a. 22(6) double cage at R3C4 = {137137} => R456C4 = 7{24} => R456C3 = {247} => 22(3) cage at R3C3 = {688}
or 22(6) double cage at R3C4 = {146146}, 4 locked for R34
-> no 4 in R3C3 + R4C2
4b. 22(3) cage at R3C3 = {499/688}
4c. 4 of {499} must be in R5C1 -> no 9 in R5C1
4d. 8 in N6 only in R45C7 -> 22(3) cage cannot be 6[88] -> no 6 in R3C3
5. 22(6) double cage at R3C4 = {137137} => R4C456 = [731] => R456C6 = 1{58}
or 22(6) double cage at R3C4 = {146146} => R4C456 = [164] => R456C6 = [482] (cannot be [428] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [639]
or 22(6) double cage at R3C4 = {146146} => R4C456 = [461] => R456C6 = [185] (cannot be [158] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [639]
-> no 2 in R5C6, no 3 in R6C5
6a. 22(6) double cage at R3C4 = {137137} => R4C456 = [731] => R456C6 = [185] (cannot be [158] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [369]
or 22(6) double cage at R3C4 = {146146} => R456C5 = [639]
-> R6C5 = 9
6b. R4C2 = 9 (hidden single in N4) -> 22(3) cage at R3C3 = [994], 9 placed for D\
6c. R5C6 = 8 (hidden single in N5), R4C7 = 8 (hidden single in R4)
6d. R6C5 = 9 -> 9 in R7C46 (because of blank double cage at R6C4), locked for R7 and N8
6e. No 3,6,8 in R6C46 -> no 3,6,8 in R7C46
6f. R6C12 = [83] (hidden pair in N4)
6g. R5C1 = 4 -> 26(6) double cage at R4C3 = {157157}, locked for C34 + N45 -> R5C2 = 6, R4C1 = 2, R4C4 = 1 (hidden single in N5), placed for D\, R4C6 = 4, placed for D/, R5C5 = 3, placed for both diagonals, R6C6 = 2, placed for D\, R4C5 = 6, R5C3 = 1
6h. R4C456 = [164] -> 22(6) double cage at R3C4 = {146146}, locked for R3 and N2
7a. Naked pair {57} in R6C34, locked for R6 -> R6C7 = 4, R5C7 = 2, R3C7 = 5, placed for D/, R6C4 = 7, placed for D/
7b. R6C456 = [792] -> blank double cage at R6C4 = {279279}, 2,7 locked for R7 and N8 -> R7C7 = 6, placed for D\, R7C3 = 8, placed for D/
7c. R3C1 = 7, R1C1 = 5, placed for D\, R3C2 = 2, R8C2 = 1, placed for D/, R7C12 = [35], R1C2 = 8, R2C2 = 4, placed for D\, R12C3 = [36], R8C3 = 4
7d. R1C4 = 9, R7C4 = 2, R2C4 = 3, R7C5 = 7, R8C5 = 5, R8C46 = [83]
and the rest is naked singles, without using the diagonals or NC.