SOFR observation lag

SOFR is observed with a 1d lag, i.e. the rate for the fixing date 2021-04-22 (Thursday) is published on 2021-04-26 (Monday). The same holds for SONIA, TONA and ESTER.

I wonder if - in principle - we need to account for the lag in the sense that the fixing on "evaluation date - 1" might exist or might have to be projected on a curve, similar to what is done for 0d - lagged indices (e.g. USD-LIbor-3M) w.r.t. to the evaluation date itself. And if so, should the yield curve start at -1D instead of today?

One might ignore the issue as long as it is ensured that one never prices at a time where the SOFR fixing for the previous day is not yet published.

What do people think?