hi, welcome to RU :wave:
yea tbh id def cut out the carrot. its not a necessity and should be a treat. its very high in sugars and calcium which aren't great for the bun. usually most people only suggest a pound coin size piece of carrot/fruit per week as a treat, not every day. it wouldn't do him any harm to just stop it, it probably be better health wise for him
dried forage however is great and can be fed frequently. it makes hay interesting and encourages natural foraging behaviour. I offer a mix of different types, roots, dried leaves twigs, flowers & so fourth. you can find them in pets at home for rather cheap (and they often have deals on). I would stay away from any seed forage (bad) and any fruit/veggie forage. they'll be high in sugars and wouldn't be great for an everyday additive type of thing.
if he hasn't been fed any hay, I do have to wonder though if his teeth are in a fit state? the back ones are often the ones that cause the issues as they are grinded down by hay, which is a side to side motion. pellet and veggies make a rabbit do an up and down motion, which is why in dental buns they might be willing to eat hard things such as pellet, but not hay. if his teeth are in a sorry state, they'll need to be operated on. no amount of different hays will tempt him to eat if its painful.
hay cookies are good but they make a mess and can get quite costly. for the amount that they need a pack isn't gong to last long. rabbits should be eating their size in hay per day, so depending on the size of a rabbit a pack may only last 1-2 days. I often offer mine as a on the side / treat. while they hay cookies do make a side to side motion when they eat, its only small pieces. I would imagine that a long strand of hay may be much better, but thats purely speculation. but as said, those are rich in alfa hay and meant for horses, so not ideal. the ones commonly used for rabbits are these:
http://www.petsathome.com/shop/en/pets/woodlands-hay-cookies-1kg
https://www.wilko.com/en-uk/wilko-small-animal-meadow-hay-rolls-7pk-1kg/p/0280986
tbh with you, I wouldn't bother with the hays in pets at home. they're often old and not great quality, they don't smell nice and they don't look fresh either. they're often chopped, so short strands of hay. it makes a huge mess and often buns seem to prefer longer strands of hay! if you can, I would suggest seeing if there is an equine stores around you as they'll sell big bags of baled hay, probably from last years crop. that way you know its fresh, and it works out cheaper too. or, farms around you may be worth a shot as they often have hay, and its well worth the money.
if not, you do have
https://www.timothyhay.co.uk but they are closed for christmas now.. they have timothy hay and oat hay, even different cuts. its always great quality.
you also have
https://www.hay-and-straw.co.uk - my personal go too. mine love the ings hay and I often rotate between ings and timothy hay.
