pathfinder 1e – Do the effects of spells that change attitude stack?

They would be friendly unless Telempathic Projection would cause them to be helpful

…but Charm will last much longer, and still last even when telempathic projection ends.

All magic affects targets in at their ‘base level’ (not a game term, but what works in my head). Magic does not build on other magic unless it explicitly says so. Per the rules on Stacking Effects

Same Effect More than Once in Different Strengths
In cases when two or more identical spells are operating in the same area or on the same target, but at different strengths, only the one with the highest strength applies.

Same Effect with Differing Results
The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.

One Effect Makes Another Irrelevant
Sometimes, one spell can render a later spell irrelevant. Both spells are still active, but one has rendered the other useless in some fashion.

Either Charm or T.P. will have a greater strength at accomplishing the same thing (temporarily altering the target’s attitude toward you). Regardless of which spell it is, both will be ‘in effect’ for their duration. In the case where they would both make the target Friendly, then the last spell is ‘officially’ active, if that becomes important.

These two spells, used together on a creature that wasn’t already Friendly, would not allow you to use Carry Companion on them.