Preview's tape deck lives on Posts' site headers, so starting hugo server means a tab switch. Here are three places it could sit on Tasks. There's one server per site, so press ▶ in any panel and the other two show it running, as the app would. Click the port to open the preview, and ■ to stop it.
Proposed
A, on the focus card, when the focus is a post or a task in a site. A post's focus card has no box (a file's focus finishes with its last task), so the deck takes the box's corner. When the focus is a task in a site's project, the deck sits left of its box. This is where the writing day starts, so it's the spot most likely to be remembered.
B, on the site's group header, on Today and All tasks. Shown only while the server runs (the switch above shows the other choice), so a running preview can be seen and stopped from Tasks without a ▶ on every site's group.
C, on the site's own scope, as a row of its health and plan card. "Preview" with the deck, and hugo's error line under it when a start fails, with the same links Posts gives.
Recommended: all three, with B only while running. ▶ to start is on the focus card and the project's card. A running server shows wherever its site does.
Only sites you've turned on with Show Posts get a deck, and only when the site is a project (its group exists on Tasks).
Open questions
Take all three places, A, B and C? (yes, or name the ones to keep)
On the group header (B), show the deck only while the server runs, or always, with a faint ▶ when stopped? (running or always)
On the focus card (A), should Preview open the focused post's own page rather than the site's home? (yes/no; recommended yes when the focus is a post, the home otherwise)