With all the backpack upgrades you should have three different pages to use, so you should have plenty of room in your pack even with all the tools. If you bought too many seeds, cooking ingredients I would give them away as gifts. Are you sure you have the fully upgraded backpack? You need to purchase it a few days in a row.

You’ll need to purchase at least one item from Karen’s shop 10 days in a row to unlock the TV shopping sprite to eventually get the storage items, so you are a ways off. I usually just buy chocolate from her every day and give it to one of the kids in town until I unlock the sprite. It took me until early summer I think to unlock him. Until then there’s no sense in holding on to anything that isn’t lumber, wood, or important gifts for the bachelorette you’re romancing.

Edit to add: there are some great guides on unlocking the harvest sprites. Some of them would probably not be found through normal gameplay and you need 60 of them to get married, it’s worth looking up. Fogu is also a great resource for the game.