Slow performance when backing up to a network share is mainly down to SMB. Without its improvement, Time Machine over a network is still dead in the water.
APFS
Provided it doesn’t have to back up large folders containing many small files, Time Machine backing up to APFS on a network share works well.
The first full backup is performed as a manual backup, and largely occurs in file-by-file copying from source to the backup store. It is more efficient than to HFS+, but differences could be less than 10%.
A summary of the known benefits and current limitations of Time Machine backups to APFS, with links to more detailed accounts.
Sparse bundles, sparse files, and sparse matrices explained in a nutshell, and how a sparse bundle could have a band which is a sparse file containing a sparse matrix.
Does Big Sur’s Time Machine preserve sparse files and clones when backing up to APFS volumes?
Adds support for reporting whether a file is a sparse file, or has been cloned, in Big Sur.
New version searches for sparse files and clones, reporting their individual sizes and totals for the folder or volume examined.
Can APFS really store more on disk using sparse files and clones? Is there such a thing as a free lunch, or do these tricks have a cost?
APFS can ‘clone’ files when copying or duplicating them within the same volume. But how can you tell whether any given file is a clone?
The Eclectic Light Company 