any thoughts?

Tongari  Suggested by jtothegriff 
Hogwarts  Suggested by traspire 
hogwart legacy  Suggested by darcoszx 
Tautz  Suggested by PePendejo émd 
University Oldstyle  Suggested by Morris Kaycee 

It's University Oldstyle Bold for the "LEGACY" and Some Letters in "HOGWARTS"

The "HOGWARTS" text is a customised version of 'Tongari'. The work was done by Pentagram, who have done the logos for Fantastic Beasts and other Harry Potter games.
Here's their write up on the work: https://www.pentagram.com/work/hogwarts-legacy/story

It doesn't state which font was used for "LEGACY", however.

Hi, the font used in "LEGACY" is the 'Tautz' font since the E text is modified and was cut (so to speak) but in itself, that is the font used in the "LEGACY" logo.