Why doing the Engine suggested move worsen my position? It is going from #26 through +60 to +9. Thats all engines best moves with deep analysis. Schould it not be a forced checkmate if I will follow the engine evaluation?
Stockfish (at a search depth of 99 moves) evaluates the initial position as actually a mate-in-19.

[FEN "2n5/1p6/1P3k2/R1K1p1p1/2p1PpPp/5P1P/8/8 w - - 4 1"]

1.Ra8 Ne7 Kxc4 Nc6 Kc5 Ke7 Rc8 Nd8 Kd5 Ne6 Kxe5 Kd7 Kd5 Ke7 Re8+ Kxe8 Kxe6 Kf8 e5 Kg7 Kd6 Kg8 e6 Kf8 Kd7 Kg8 e7 Kf7 e8=Q+ Kf6 Kd6 Kg7 Ke7 Kh6 Kf8 Kh7 Qh5#


The next position is a mate in 18 moves.

[FEN "R7/1p2n3/1P3k2/2K1p1p1/2p1PpPp/5P1P/8/8 w - - 6 2"]

1.Kxc4 Nc6 Kc5 Ke7 Rc8 Nd8 Kd5 Ne6 Kxe5 Kd7 Kd5 Ke7 Re8+ Kxe8 Kxe6 Kf8 e5 Kg7 Kd6 Kg8 e6 Kf8 Kd7 Kg8 e7 Kf7 e8=Q+ Kf6 Kd6 Kg7 Ke7 Kh6 Kf8 Kh7 Qh5#


The final position is mate in 17 moves.

[FEN "R7/1p6/1Pn2k2/4p1p1/2K1PpPp/5P1P/8/8 w - - 1 3"]

1.Kc5 Ke7 Rc8 Nd8 Kd5 Ne6 Kxe5 Kd7 Kd5 Ke7 Re8+ Kxe8 Kxe6 Kf8 e5 Kg7 Kd6 Kg8 e6 Kf8 Kd7 Kg8 e7 Kf7 e8=Q+ Kf6 Kd6 Kg7 Ke7 Kh6 Kf8 Kh7 Qh5#


You probably didn't give the engine sufficient time to find the mate.

Another important fact to note is that the Lichess app uses the javascript version of Stockfish. The problem with this version is that it cannot make use of hash tables. So when the engine evaluates a position and then left to evaluate another position resulting from a move in the initial position, it evaluates the position as if it was restarted before evaluation. I am pretty sure if you give the engine some time to evaluate the second and last positions it will come up with the mate.