Do I need to upgrade the database？
It is not necessary, that is a different database. Database which AlphaFold uses for inference of a new structure hasn't changed, only database that contains already predicted structures is growing but that one is not used by AlphaFold for future predictions.  I thought, that the --max_template_date corresponds to the deposition date in the pdb. And the local copy of the pdb database is used for compiling MSA, so maybe it would be useful to update this from time to time.

Considering the more and more protein structures deposited in PDB, do I need to upgrede my AlphaFold database? and how to?