How approval is calculated is somewhat of a mystery to me. One thing for sure though is it 10% higher when I have an approval relic being mined by a starbase, yet it doesn't say it is. I decommission the starbase and the approvals for all colonies go down 10%.
In contrast, if you have a culture relic, the colony info does show it increasing influence by 10%. So this too leads me to believe approval relic is missing in the list of things that modify approval.