When talking about spinning disk media such as floppy and hard disks ...
"Spinning disk media" is an overly descriptive term. Solid State Drives and other mass-storage devices emulate HDDs, so some of these terms can be used in relation to these devices as well.
allocation unit
This is actually a filesystem (for random-access device) term rather than a disk or mass storage term.
The filesystem is what manages the storage device, and needs to maintain an accounting of what is in use (and by which file) and what is available.
For simplicity an allocation unit will consist of a fixed number of consecutively addressed, physical storage blocks, aka sectors. This provides a simple arithmetic translation between the allocation-unit number and the starting sector number (or LBA).
If the sectors (or LBAs) were not consecutively numbered, then each allocation unit would need its own sub-allocation list (which would be absurd).
As a filesystem term, this is a generic concept that transcends any implementation.
This term, in the form of of the acronym AU, is also used by the NAND Flash Translation layer in SD cards when used in video storage mode (as described in the SD Specifications, Part 1, Physical Layer Simplified Specification). In this situation the the NFTL is providing a filesystem-like service to emulate a sequential-access medium (like tape) using a random-access medium for recording video.
block
This is a word that has many meanings and uses in computer programming, computer hardware, and communications.
The meaning of "block" even when specifying a context such as in regards to disk drives is still ambiguous.
Without context and a qualifying descriptor or adjective preceding it, this word has no specific definition other than some grouping of bytes or data.
The Wikipedia article you cite tries to explain that the term 'block' has several meanings as a noun but is incomplete.
The article ignores the usage of 'block' for logical constructs, such as an arbitrary-sized logical block consisting of several LBAs, or allocating a block of memory (which is not defined by physical boundaries). For instance the Linux man page for malloc(3) mentions 'block' (of memory) 7 times.
The article has a redirect for the usage of 'block' as a verb relating to process scheduling, such as blocking (suspending) a process due to a pending I/O operation.
The ext4 reference cited in another answer is a perfect example of the multiple meanings/usage of the term 'block'.
In a specific context that document tries to convey that 'block' refers the unit of allocation for the ext4 filesystem.
But the word 'block' is still used for alternate meanings but qualified, such as the Super Block, and journal entries called Descriptor Block, Revocation Block, and Commit Block. The lengths of these 'blocks' are unrelated to the allocation 'block' size.
See also an old answer of mine on 'blocks'.
cluster
Because of the ubiquity of Microsoft operating systems and filesystems on PCs, the term cluster is widely understood to be a unit of allocation (for files).
Perhaps less understood is that this definition actually only applies to the FAT or NTFS filesystems.
granule
I'm not familiar with this term, but the reference you provide clearly states that this is the unit of allocation for files on diskette.
would "allocation unit" be the best umbrella term to be universally understood across platforms?
Yes.