I think yes. While many companies have unprefixed titles, others have just plain "Software Engineer" as one step above graduate and even some otherwise decent companies will discard resumes applying for senior/lead positions when a HR drone does a first pass and decides "no senior level experience", even if your descriptions are full of business impact and leadership experience.

I think it's also important to know what you're applying to too.

If you're applying to a Frontend Engineer Position, and you're a Software Engineer who's comfortable with both parts and the full stack, you just shut up, put frontend engineer in the CV, and let them choose you, you can always tell them you also know to do backend stuff on the interview....

First passes are pretty simple, they just match their job position with the stuff recieved.

ATS filter you based on keywords before a human does

Yeah, honestly if I was coming from a startup that called everyone the Vice-President of Whatever (or indeed a large multinational bank; some of those also have silly title inflation) I'd be inclined to just put engineer.