comparison of gain in db to dbi
The gain dB in the Friis formula is the same as the gain you mentioned in terms of dBi.
As you are already aware of isotropic antenna is an ideal antenna spread evenly across the sphere. This is the situation where 0dBi happens.
As you also aware in practical, 0dBi never happens due to assymetric of feeding structures, physical size of the antenna etc..
In Friis formula, it assumes the equation to be an ideal isotropic antenna, so ideally the equation should be ended up 0 on both sides, due to the conservation of energy.
So anything creating imbalance in the friis formula, it assumes to be the antenna gain (dB = gain of something unknown, or dBi = gain from the isotropic antenna).
Of course this is most likely not the case depends on your path loss models.