An important update on 8-Men Tablebase by Marc Bourzutschky.
This is worth reading in detail, but one point demands quotation:
An important question is at what point the chess board becomes so crowded that adding more pieces does not lead to longer winning lines due to the increased likelihood of shortening captures. My results suggest that we may already be at or close to this saturation point: the longest winning line for 8-man endgames without pawns appears to be “only” 400 moves. [...] After generating about 15% of the pawnless endings I’m quite confident to have captured the longest ones. While 15% seems like a small subset at first blush, most other piece configurations have large material differences between White and Black so that long lines are unlikely.
Q: How long is the longest forced checkmate in chess?
A: We will probably never know but the naive extrapolation based on multiplication by number of moves is no longer impossible. It is even conceivable that we already know the longest forced mate in all of chess, which occurs with 7 pieces.
50/75 move-rules don't apply
Firstly, let's definitively remove one distraction: 50-moves (or 75-moves). The Codex for Chess Problem Compositions states:
Presently the rules defined in the 1 Jan 2018 version of the FIDE Laws are valid. > Relevant for compositional chess are articles 1 to 5, 9.2 and 9.3.
This includes 50 moves-rule, but excludes 75 moves-rule. However:
Article 17 – 50 Moves-Rule
Unless expressly stipulated, the 50 moves-rule does not apply to the solution of
chess compositions except for retro-problems.
These conventions are specifically crafted to support the kind of endgame analysis being discussed in this SE question.
The answers are very different from a superficially similar SE question where the 50 move-rule is taken into account.
Extrapolation from 7-man
The 7-man case is solved at 549 moves, and ingenuity has pushed this back a few more moves (as of Jan 2021, 535 moves). The real breakthrough will come from tablebase development for the 8-man case. We don't know what the answer will be, but there is some intelligent extrapolation possible from existing results.
The Lemonosov webpage stated as long ago as 2014:
Many show interest in what to expect from 8-man endings. First, take note that the longest
6-man mate took 262 moves (KRN-KNN). Moving to 7-man endings doubled [the value].
Of course, as the number of pieces increases, it maybe that the opportunity for stalemate increases and tends to dominate. There is no indication that this is happening at 7-man database level. We are not just limited to the 32-piece starting position, of course, we are looking at any legal position where no captures have yet taken place. So chess as whole might be a draw, while at the same time there might still be some very long forced checkmates in 32-man positions.
I imagine (and it can't be more than this) that such positions might lead themselves very quickly to exchanges, because the board is so cluttered). But I have no idea, and (absent some stupendous breakthrough in quantum computing) humanity will never know.