Sure. Just look at Wordpress... it's a blogging platform rather than a forum, but it has an ActivityPub plugin available that allows federation of blog posts and comments. ActivityPub is a standard published by the W3C (the same organization that oversees the HTML standard, among many others). Anyone can implement the standard in their software if they want to.
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Small point of fact, but HTML is actually overseen by WHATWG primarily, not W3C. W3C agreed back in 2019 to just follow WHATWG's process.
You'd be asking PhpBB or Discourse to implement ActivityPub. The latter already has a plugin for it, but PhpBB doesn't have much discussion on the topic
NodeBB is also working on activitypub integration