No need for HTPC, just a small USB device with HDMI output and DLNA support. You use your phone as a DLNA controller, a server running Jellyfin as DLNA provider, and the device attached to the TV as DLNA renderer. And sometimes TVs have DLNA support built-in (my Toshiba does).
On Android there's an amazing app called BubbleUPnP that can source media from a wide variety of places, make playlists, and cast to DLNA devices as well as proprietary protocols like Chromecast.