Yo, congrats on the X-H2S, thats a beast of a body but honestly, your 600 dollar budget makes things kinda tricky for top-tier glass. I spent way too much time testing the older Fujifilm XF 56mm f/1.2 R and unfortunately, its just too sluggish for a birthday party. The autofocus hunting is real and youll probably miss half the shots of your niece blowing out candles which sucks. Heres what I found after geekin out on the MTF charts and real world use:

• Fujifilm XF 50mm f/2 R WR
• Super fast AF and tiny, but the bokeh is kinda clinical and meh for portraits imo. It just doesnt have that wow factor.
• Viltrox 75mm f/1.2 AF Fuji X
• This thing is a chunky monkey but the f1.2 light gathering is wild for the price. It actually out-resolves almost everything else in this bracket.
• Fujifilm XF 35mm f/1.4 R
• People love the magic look but the motor sounds like a coffee grinder and it feels super dated now. If you want the best face shots without breaking the bank, id probably grab the Viltrox. It hits way above its weight class even though the size is annoying and it might feel a bit front-heavy. Most of the native Fuji stuff in your price range is unfortunately showing its age or lacks that creamy background you are looking for. Just make sure you have enough room to back up because 75mm is pretty tight for indoor parties...