Should we centralize databases or have a database with each application?
What you have read (even though it's oldish) is still very relevant!

Your problem is called multi-tenancy - to do it or not - the consensus appears to be "not", but there is a wide divergence of views on this issue - you can "partially multi-tenant" - i.e. keep virtually unchanging reference tables in common for example - however the same issues as outlined below apply to "partial" multi-tenancy.

My advice - use separate databases if at all possible! 


If one app goes down, at least the others will still work, with a central database, if one app brings the server down, you're bunched (nothing will work). 
Also, for migrations, if you need to, say, migrate one of your apps (size/speed/whatever problems - or you wish to dip your toe into the cloud testing with one app), then you will have difficulty separating out your apps, whereas if you use separate systems, you won't have any difficulties on that score!


If you'd care to explore this in more detail, I have answered questions on this issue before - check them out (1, 2 and 3 and links therein). Obviously cost and the nature of the expertise readily available to you is an issue so it's worth checking out your options before coming to a decision - you 

Sometimes the wise heads are indeed on old shoulders! :-)

Another recommendation - use PostgreSQL if at all possible! It is vastly superior to MySQL in a myriad of ways - SQL compliance, JSON, Geospatial, CHECK constraints, SET operators ... long list... you won't regret it!