The decision is not whether you want a bigger title. It is whether you want your daily craft to become organisational design rather than software delivery. Directors are judged on whether the structure they built keeps producing results when they are on holiday, not on the quality of the release they personally shepherded.
That trade is real and it is not reversible on a short timescale. Two or three years of Director work leaves you with a track record in hiring, budget defence, cross functional negotiation and manager development. It leaves less recent evidence of hands on technical judgement, which narrows your options if you later want to return to a deeply technical role.
The useful question is therefore not "can I do the job" but "is the evidence I am accumulating pointing at the job I actually want in five years". Many engineering managers answer that question honestly and choose a staff or principal track instead, which is a promotion rather than a retreat.