HoT Story in PoF ?
PoF is standalone so you can ignore HoT and go directly to PoF
No, there is no need to do any HoT story, any of the HoT masteries or waste your time on HoT maps. You can, however, do some Living Story Season 3 content which you can get for few gems. LS3 and soon-to-be-released-PoF share similar map design and many gameplay elements. Also PoF story is directly continuing from LS3 story.
Don’t play the game for the story and you will save yourself a lot of headaches.
If you want to understand various ongoing plot threads (yet also be annoyed at various ones quietly being ignored), then yes, along with LWS3 you may need to pay gems for.
If you don’t care at all about plot, then no.
PoF is standalone so you can ignore HoT and go directly to PoF
However, whether the OP will fully understand the story, since all the campaigns are interconnected, is doubtful.