This topic has a long history. A very cursory search using the Brave Community search function quickly turned up, (for example)
Automatically Switch to New Tab When Opening Link
“Open link in new tab” doesn’t focus on the new tab and
Switch to New Tab When Opening Link
Do your own search. The list goes on. And on. And on… The request remains unresolved, at least by Brave.
@Sectre (in this thread) comments “I’ve seen this request as far back as 2015.” That may be a bit of a stretch. I’m unsure whether Brave had been released in 2015 …
But.
Brave initially used Muon as its engine. The Muon version of Brave did offer to automatically switch focus to a new tab when a link was opened. It was an option. Some folks didn’t / don’t like it. It’s an option. Use it or don’t use it, but give users the choice.
@ygoe (again, in this thread) suggests the add-on / extension Tabs to Front about which I know nothing. Tabs to Front may be excellent. I don’t know …
note: I've edited the following reference to Tab Activate since I posted my initial comment; explained a few comments down.
Since August 2020, I’ve been using Tab Activate:
How Tab Activate compares to Tabs to Front … I’m clueless.
Worth adding — and if you take nothing else away from this post, it’s imperitive that you pay close attention to this: Good add-ons / extensions go bad. Here are four citations:
3/1/2020 The Case for Limiting Your Browser Extensions
11/20/2020: Abusive add-ons aren’t just a Chrome and Firefox problem. Now it’s Edge’s turn
2/5/2021: A 0-day, malicious extension, and sync abuse are keeping Google developers busy.
3/1/2021 Is Your Browser Extension a Botnet Backdoor?
Again, do your own web search. Take the warnings to heart.