Have you actually tried going to the tile and seeing if you can enter them now? Because it should open up automatically without any additional action on your part needed once you've finished Dog Days.
If you've done the quest and you genuinely can't enter the garden, post a save and maybe someone can work out what's happened with your event flags.
I just tried myself with a completly fresh character. Everything works as intended. After Dog Days, I talked to Garth about "Gardening" and clicked ready. Then I got teleported to the entrance of the Garden and the fight began. You don't have to go to the garden yourself after Dog Days. I think this is where the problem lies.
Thanks bobong and wolf for your help and bobongs help fixed it btw, heres my file if you still need it, and again thanks, this seems like a pretty chill community.