If you had not mentioned the meeting another time traveler and the recency of the story, I would have sworn it is "Last Rites" by Ray Bradbury.
But it is not only indeed
"about a time traveler (possibly rogue(?)) who meets important historical figures just before their death and informs them of the importance and influence that they have on the future"
but also a haunting, deeply affecting story for anyone who likes Bradbury.
Although the other descriptions don't match, this question arrested my attention and sent me off on a search for this story about a literary, academic inventor of a time machine who wakes up with an epiphany after a night of drinking and quoting literature with a like-minded buddy.
Interesting that your search results kept producing another Ray Bradbury story.
Even though it doesn't match the other parts of the question, it is worth a mention.
His aching need is to go back to those authors - just before their death to avoid messing up their timestream - and reassure them that they will not remain unknown, but that thousands of people will still read and be moved by their words a century after their lifetime.
Harrison Cooper, seated back in the shadow of the great hovering Mobius ribbon, laughed and nodded. “Yes! Harrison Cooper, L.M.D. Literary Meadow Doctor. Curer of fine old lions off their feed, in dire need of tender love, small applause, the wine of words, all in my heart, all on my tongue. Say ‘Ah!’ So long. Good-bye!”
I never, ever forgot his quote about fine old lions gone off their feed.
He visits Melville and Poe
“Are you forgotten?” a voice asked.
“Unborn,” the pale man replied.
“Only. Only in. France.”
“Wrote nothing at all?”
“Feel the weight of what I place on your bed. No, don’t look. Feel.”
“With names, yes, but not tombstones. Not marble but paper. Dates, yes, but the day after tomorrow and tomorrow and ten thousand after that. And your name on each.”
“It will not be.”
“Is. Let me speak the names. Listen. Masque?”
“The Fall of-“ –
“Heart! My heart. Heart!”
“Repeat: for the love of God, Montresor.”
“Repeat: Montresor, for the love of God.”
“For the love of God, Montresor’.”
“Do you see this label?”
“Read the date.”
“Nineteen ninety-four. No such date.”
“Again, and the name of the wine.”
“Nineteen ninety-four. Amontillado. And my name!”
“Yes! Now shake your head. Make the fool’s-cap bells ring. Here’s mortar for the last brick. Quickly. I’m here to bury you alive with books. When death comes, how will you greet him? With a shout and-?”
“Requiescat in pace?”
“Say it again.”
“Requiescat in pace!”
The Time Wind roared, the room emptied. Nurses ran in, summoned by laughter, and tried to seize the books that weighed down his joy.
“What’s he saying?” someone cried.
And the story leaves off knowing that he is visiting yet more authors.