Capcom will be presenting their E3 2021 showcase live on June 14th at 2:30 PDT (US time). The stream will feature news on their latest games, including the recently announced The Great Ace Attorney, Monster Hunter Stories 2, Monster Hunter Rise and Resident Evil Village.
No word if we'll see anything from the Mega Man front. However, we are anticipating the next major title in the franchise to launch between mid to late 2022. Tentatively dubbed "Rockman Taisen" (Taisen in this context= "versus", "war", "bout", "battle" "match-up"), this elusive project came to light during the November 2020 data breach. It's still a ways out there so no telling if E3 2021 is too soon or not.
We also have the unannounced Rockman X DiVE Steam port. I don't see E3 as the "right" venue for that kind of announcement, though. Maybe one of the DiVE YouTube streams we hear from time to time. Your guess is as good as mine.
In terms of Mega Man Battle Network stuff... eh. I wouldn't be too hopeful. We're still in the thick of the recently-confirmed delayed. Considering we've yet to hear anything from certain partner products -- the highly-anticipated Rockman.EXE Kotobukiya kit comes to mind -- I don't foresee E3 being the end-all-be all moment we've been waiting for. I really think these delayed announcements will be grouped together via a Rockman Unity Twitter thread, a post or something. E3 is not the place.
Whether or not E3 brings news, take heart that there's different things in the pipeline. We shall see.