I’ve never heard of it done the way you propose, but I don’t see why you couldn’t. Everything is worth a try imo. My only concern is that you’re reading a dynamic into the model that the model didn’t actually fit, and thus it could just be random noise. Whatever the difference of the last two posterior values of the GRW happen to be will lead to a deterministic trend, but the model doesn’t “know” anything about this trend term so it’s questionable whether you have evidence that it exists. In addition, since you don’t model the mean of the GRW, I think the differences will always be mean zero, but it’s late and I didn’t do anything to verify this intuition so I could be wrong.
One note, though, is that models that include a trend which extrapolates out from last observed trend tend to forecast poorly, and many time series models introduce a “dampened trend” to correct for this. See the discussion here. This is close to what you are proposing, so I also think you should be cautious about naively extrapolating a trend from the GRW posterior for this reason. (I’m not suggesting you should worry about a dampened trend in your model, just pointing out that trend extrapolation isn’t so simple)
If I were going to add a trend to your model, I would either include a deterministic time trend in the model (this is what you suggest in the 2nd point), or explicitly model the mean of the rw_innovations (I guess people call that a “drift”, though if you do the algebra it comes to the same thing; i call this \mu in the post I linked). The mean itself could also be a GRW, then you’d get something like a “local level” model where you estimate both the “speed” and “velocity” of the process. I think this is close to what you are thinking about with the “corrections” approach.
With either of these approaches you don’t need to worry about any complicated post-processing. The trend will just fall out of the estimation and can be used to forecast.