Two things:

-there might be a bubble term

-all the adjustment could come through discount rates rather than cash flows

Assuming the existence of a pricing kernel (i.e. a stochastic discount factor), isn't it pretty much obvious that the government debt valuation equation (i.e. the intertemporal budget constraint) must hold with equality?

Obviously, this doesn't say what the SDF is, and how should we model it, but on a philosophical level, fiscal theory of price level should then be necessarily true, when using the correct SDF, right?

In principle, yes, there could be a bubble term in an infinite period model. In practice, the future of the universe is finite, and in the last period, the gov't can always cover any remaining debt by printing money (which is exactly the source of FTPL), so the possibility of a bubble does not seem that relevant.

Yes, all the adjustments can come through discount rates, but it still doesn't violate the theory, does it? I.e. the price level (valuation) equation still holds.