In InnoDB, how does fuzzy checkpointing's recovery consistency work?
(I'm pretty sure of the following.)

InnoDB does not depend on "dirty" pages for recovery.  Recovery is guaranteed by what is stored in iblog* and the double-write buffer.

The presumption is that the information about a transaction can be more compactly stored, and more rapidly written to disk, in the redo log (versus the actual table).

The log files are overwritten, but not until LNS says it is OK.  So, the optimal dirty page to flush is either the "least recently used" or the one with the oldest position in the log.  I don't know what algorithm it uses to decide between these conflicting things.

If there is a lot of activity causing the percentage of the buffer_pool to be 'too close' to 100% dirty, InnoDB shifts gears and becomes more aggressive at flushing dirty pages.  This, also, is a tradeoff.

Note also that the writing of changes to non-unique secondary indexes is also 'delayed'.  This is in the "change buffer", which (by default) occupies 25% of the buffer_pool.  The hope with that is that the updates can be somewhat sorted and written to disk with fewer read-modify-write cycles.  Again, recovery does not depend on this having been completely flushed to disk, and the redo log is the critical part.

The double-write buffer protects against "torn-pages".  This is a potentially disastrous situation where the disk subsystem write can't write all 16KB in an atomic operation.  A few newer disks guarantee atomicity, so the setting can be turned off.

InnoDB is crash-proof.  But, it is also "fast" because of delaying I/O, together with these various techniques that work efficiently under high load.