I have to side with Mark17 on this question. The wording is not cut and dry, as the phrase in question could be describing “the church of the living God”, or simply the directly preceding “the living God”.
So I think this is a case where one needs to look to the rest of Scripture to see which is the more likely interpretation. It is God, not the church, that is consistently described in the rest of Scripture with symbols like “the rock”, “the chief cornerstone”, “the sure foundation”, etc. So, I think it is more in line with the rest of Scripture to read this description as meant to apply to God, not the church.
I always try to interpret the more difficult to understand verses, in light of the clear teaching of the Bible, not the other way around. Make sense?
"the assembly of God the living the pillar and base of the truth"
We can then look at Paul's letter to the Ephesians.
Ephesians 2:19 Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God; 20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;
Building on that foundation would be the pillars or the parts that hold up. It would difficult to discount either view imo.