Mate in 125

What about draw by 50 move rule?
I don't know if there was one when this endgame was made but today there is not. The endgame is composed and not cited from a game. The 50-move rule is canceled for compositions which gives room to very long endings like this one and many others you'll find e.g. in tablebases.
This appears to be a correct composition as the position is legal - it could occur in a game. Otto Blathy quite often crossed the legality line as he set his own standard for sound positions.

bruh I know someone necroposted on an 8 year old thread but that's pretty cool so I'm glad I stumbled upon this lol
draw by 50 move, also draw by 100 rule when that was a thing
Dream on. There are no such rules for endgame studies. The 100-move game draw rule was adopted briefly for the 2N vs P endgame by arbiters (I was told) but never made the FIDE game laws which can be checked in the archives. When all kinds of new "frustrated win" endgames popped up after computer analysis, the attempts to list them as exceptions were abandoned. Now there is only the 50-move line. Everyone is welcome to feel "frustrated".

draw by 50 move, also draw by 100 rule when that was a thing
Dream on. There are no such rules for endgame studies. The 100-move game draw rule was adopted briefly for the 2N vs P endgame by arbiters (I was told) but never made the FIDE game laws which can be checked in the archives. When all kinds of new "frustrated win" endgames popped up after computer analysis, the attempts to list them as exceptions were abandoned. Now there is only the 50-move line. Everyone is welcome to feel "frustrated".
You are correct about the 50 move rule for studies, I think they also call a win that exceeds the 50 move rule a "cursed win".

Here is a mate in 87 move study by Blathy that I found a "dual" in with Stockfish (well Stockfish did all of the work) from the root position, it's a mate in 22.
96/44 14:38 17,925,823k 20,404k +M22 1.Qc3xc4 Qa3-b2 2.Ne2-c3+ Ka4-a3 3.Nc3xb5+ Ka3-a2 4.Bd1xb3+ Na1xb3 5.Nb5-c3+ Ka2-a3 6.Qc4xa6+ Nb3-a5 7.b4xa5 Qb2xc3 8.a5xb6+ Ka3-b3 9.b6-b7 Bd6-c7 10.Qa6-b5+ Kb3-c2 11.Qb5-e2+ Qc3-d2 12.Nc6-b4+ Kc2-c3 13.Nb4-a2+ Qd2xa2 14.Qe2xa2 Kc3-d3 15.Qa2-d5+ Kd3-e3 16.Qd5-c5+ Ke3-f4 17.Qc5xc7 g6-g5 18.b7-b8Q Kf4-f5 19.Qc7xe5+ Kf5-g4 20.Qe5-e4+ Kg4-h3 21.Qe4-f3+ Kh3-h4 22.Qb8-g3+
Here is a mate in 87 move study by Blathy that I found a "dual" in with Stockfish (well Stockfish did all of the work) from the root position, it's a mate in 22.
Well done nevertheless! With SF doing the calculations, we have kept the best parts to ourselves. First we have to identify the promising suspects knowing history and context and our own chess intuition. Often we also need to select the parts to test which sometimes requires amendments to the position. Finally we like to take on the challenge of correcting them when flawed and gain ownership of a creation to which we merely contributed a pawn or a move . I fixed an "illegal position" 102-mover by Blathy at the cost of 2 full moves. But the ton is still mine!
Btw, any chance to fix this one? The gap between 22 and 87 is probably too wide!
You are correct about the 50 move rule for studies, I think they also call a win that exceeds the 50 move rule a "cursed win".
There are no "frustrated" (where did I get this term from?) or "cursed" wins in endgame studies. But of course when you refer to the tablebase for the outcome of a particular variation you will hit on the way the tablebase GUI structures its solutions. Which may create the illusion that the study has "cursed win" variations!

Here is a mate in 87 move study by Blathy that I found a "dual" in with Stockfish (well Stockfish did all of the work) from the root position, it's a mate in 22.
Well done nevertheless! With SF doing the calculations, we have kept the best parts to ourselves. First we have to identify the promising suspects knowing history and context and our own chess intuition. Often we also need to select the parts to test which sometimes requires amendments to the position. Finally we like to take on the challenge of correcting them when flawed and gain ownership of a creation to which we merely contributed a pawn or a move . I fixed an "illegal position" 102-mover by Blathy at the cost of 2 full moves. But the ton is still mine!
Btw, any chance to fix this one? The gap between 22 and 87 is probably too wide!
I'll have to fiddle around with it when I get home.