I've been looking a bit myself at daypacks (I've been using an Under Armour rucksack and whilst it's fine I'm fed up with a sweaty back and that's even in the winter) so have decided to go for a haversack/satchel, which seem to be very popular with the bushcraft community and so often have the axe loops.
https://www.helikon-tex.com/en_eur/tb-bst-cd-bushcraft-satchel-bag-cordura.htmlThat's the one I'm looking at, it's a wee bit smaller than you want at 17L but what I like is that it has MOLLE webbing on both ends so things like my BCB Crusader cookset and pouch with my first aid kit/toilet roll/hand gel/fire kit can be carried on the outside if there isn't enough space inside. Outside pockets on both ends, one closed and one open at the bottom for carrying an axe.
Haven't taken the plunge yet on that one, I've been using an old military surplus Polish Bread Bag that I got for the princely sum of £4 from Military Mart, wanted to make sure I felt comfortable with a haversack before splashing out £50.