Yes you can have a feat but why are you taking polearm master when you don't have any appropriate weapons to use it with? You have a great sword.

i think switching to polearm is necessary for Cats path of the world tree barbarian stuff later.
and reach is always good for sentinel

Exactly!
It will take until level 10 though but then Cat will have 20ft reach with a polearm. For now the 10ft reach with a polearm is good enough. Bonus action pole strike (1D4+Rage dmg) after each attack and a reaction attack against a creature that enters Cat's reach. Per Joy's rule there are unlimited opportunity attacks. Any enemy that goes within 10ft (and 20ft from level 10) of Cat will get auto-attacked. Combined with Sweep and Sentinel the extended reach will be pretty awesome.
You are right Cat will have to find of buy a slashing polearm weapon like a glaive though. We also need to buy smiths and carpenters tools

Cat will gain an extra attack and fast movement. Sorry for not memorizing your rules again but it's been half a year since our last level-up. Will you grant Cat another feat / proficiency?
I have the following suggestions, open to discussion:

Carpenter's Tools (8 GP)
Ability: Strength
Weight 5 lb.
Utilize: Seal or pry open a door or container (DC 20)
Craft: Club, Greatclub, Quarterstaff, Barrel, Chest, Ladder, Pole, Portable Ram, Torch

Polearm Master
General Feat (Prerequisite: Level 4+, Strength or Dexterity 13+)
You gain the following benefits.
Ability Score lncrease. Increase your Dexterity or
Strength score by 1, to a maximum of 20. [Cat takes DEX as her STR is maxed out]
Pole Strike. Immediately after you take the Attack action and attack with a Quarterstaff, a Spear, or a weapon that has the Heavy and Reach properties, you can use a Bonus Action to make a melee attack with the opposite end of the weapon. The weapon deals Bludgeoning damage, and the weapon's damage die for this attack is a d4.
Reactive Strike. While you're holding a Quarterstaff, a Spear, or a weapon that has the Heavy and Reach properties, you can take a Reaction to make one melee attack against a creature that enters the reach you have with that weapon.

Ah, that came unexpectedly fast!
I'll discuss that with Cat but I won't make it today!

Good. I suggest we take a short rest until the skull returns. If it doesn't we have to go search it.

You should have said that sooner! I have a good view Southwest. I'll try now, Sun will set in about an hour. But there are a few clouds.

That was easier than thought. Is Emboldening Bond still in effect? I think it was broken when Alice was teleported.

Did you watch the Starship test flight? Finally something I could see live because it was Saturday morning.