Job application dilemma

hey all! I’ve been applying to jobs for a while (currently on OPT with 30 more days of unemployment left) and I stopped responding YES to the infamous “will you require sponsorship now or in the future”. The reason I did so was because even E-verify companies that could grant my STEM OPT extension later on would automatically reject me thinking I need sponsorship in the immediate future.

Currently I’m interviewing for a lot of places under the assumption that I won’t need sponsorship now or in the future.

My question is, do I wait till I reach the offer stage at these firms to let them know that I will technically need to be sponsored after 3 years? Do I tell them that I am not sure I’ll need to be sponsored (just STEM OPT supported) given that I’d be interested in pursuing masters education after my 3 years?

Any perspective helps, thanks!