How do I set a path alias for each forum?
It is possible to add a path alias to a forum, without installing any third-party modules.
You could install the Pathauto module, but that is more for automatically assigning the path aliases when creating/editing an entity, or for bulk-assigning path aliases to existing entities. If you install the Pathauto module to create path aliases for the forums, notice that under Enabled entity types on /admin/config/search/path/settings, you don't see an entry like Forum. Use the default values for that form field (which include Content and Taxonomy term that you cannot deselect), and you will be able to set path aliases for the forums.


  


It is a quite confusing, since in /admin/config/search/path/patterns/add you need to select Forum for Pattern type.


  


Maybe it would be less confusing if Forum would be an option for Enabled entity types too. 

In this case, anyway, the path aliases that the Pathauto module says to assign to forums are really assigned to the taxonomy terms associated with the forums. The effect of this is that the /forum page would not use any path alias for the forum links.

I created a sandbox site on simplytest.me, and I just enabled the Forum module. I created two forums (Module development and Theme development), and created a forum topic (Porting the "User activity" module to Drupal 8). I went to /admin/config/search/path, and created the following path aliases.


/forums/1/general-discussion pointing to /forum/1
/forums/2/module-development pointing to /forum/2
/forums/3/theme-development pointing to /forum/3


Doing so, the /forum page used the path aliases I set, in the links to the forums, but the forum topic pages used links like https://dsze.ply.st/taxonomy/term/2 under Forums.

So, or you set a path alias that is used from the /forum page (but not from the forum topic pages), or you set a path alias that is used from the forum topics page (but not from the /forum page), or you set two different sets of path aliases (a set used from the /forum page, and a set used in the forum topic pages).