Donald J. Trump has long been a man undone by himself.

He imperiled his presidency and political campaigns with personal grudges, impulsiveness and an appetite for authoritarianism. His casual approach to the rule of law — and unwillingness to accept electoral defeat — resulted in $83 million in penalties, nearly three dozen felony convictions and additional legal trouble ahead.

But on Thursday night, with his right ear still bandaged five days after he was wounded by a would-be assassin’s bullet, Mr. Trump attempted a politically cunning transformation.

He opened his address by casting himself as a unifying figure, promising to bridge political divides he had long delighted in deepening. He mentioned President Biden by name only once. At brief moments, he struck tones more similar to President Barack Obama’s message of hope and healing than to the dark version of America that Mr. Trump described in accepting his first two Republican presidential nominations.

“The discord and division in our society must be healed — we must heal it quickly,” Mr. Trump said on the Republican convention’s final night. “As Americans, we are bound together by a single fate and a shared destiny. We rise together — or we fall apart.”

With the Democrats divided and polls tipping in Mr. Trump’s favor, Republicans used their national gathering in Milwaukee to bask in the moment. In their view, Mr. Trump — twice impeached, repeatedly indicted, convicted, fined and soon to be sentenced — appears on the verge of regaining control of the world’s most powerful office.