Is it possible to break down query time?
Not really.  But...

Use PHP's microtime(true) to give you precise times.  Then time trivial things such as SELECT 1.  This should give you a feel for the "network roundtrip time".  That is effectively added (once) to each SELECT that you do.

As for queries getting slower...  Look at whether the tables are getting bigger.  Look at the EXPLAIN plans to see what counts it estimates.  Look at the algorithms to see if they are O(1), O(N), or O(N*N), etc.

By "cluster" do you mean "NDB cluster"?  Or "Galera Cluster"?  Or something else?

Another tool is to do this:

FLUSH STATUS;
SELECT ...
SHOW SESSION STATUS LIKE 'Handler%';


This gives a precise count of the number of rows (index or data) that need to be read/written to perform the SELECT.  Track that over time to see if it is growing due to data size growth (as opposed to something else making things sluggish).