This might be the mildly infamous "Harry Potter and the Psychic Serpent", which gained some small renown for being released in an ebook package as the fifth book of the series along with the actual first four books. It does start with Harry working with a group of landscapers at the Dursleys with him noticing himself more muscled. In the second chapter, Ginny sends him an amulet in a letter. And yes, he does eventually become a Griffin Animagus.
Here is the summary from Fanlore:
In Harry’s fifth year at Hogwarts, he gets a snake with the Sight; Hermione’s torn between Ron and Harry, who's torn between her and Ginny, who's torn between him and Draco Malfoy, who's torn between her and loyalty to his father. Voldemort may be trying to recruit Harry now instead of killing him, and there are giants and house elves and a Duelling Club.
And it does involve Dumbledore awarding them with the "Order of the Phoenix":
He held up a small gold-colored brooch with the letters OP in the middle, flanked by wings with red enamel over the gold metal, and what seemed to be flames coming up from the letters, also with enamel, but rather than being a single color, the flames actually looked like flames, moving and changing every second, white and yellow and red and orange and sometimes a little purplish-blue. They all stared dumbly at the headmaster, unsure what to make of this. He sighed and held it out to Ron, then took others out of his pockets and distributed them round to the rest of them.
"It's the Order of the Phoenix. Now, I know it's not the Order of Merlin, but I really couldn't nominate the five of you for that—you broke too many rules along the way." His eyes twinkled at them. "So I made up my own Order of the Phoenix, to recognize the work of people who have dedicated themselves to bringing dark wizards to justice. I know that to young people, an award like this is a piddling thing. It's not hundreds of galleons or a chance to meet your favorite Quidditch player, I'll grant you that. But it's my way of saying thank you, that I think we're fighting on the same side and that I trust you to do the right thing. Oh, and I'm also having house elves work on some lovely parchments that can be framed and hung on the wall.
FWIW, I ran into this by searching for harry potter "griffin animagus" "order of the phoenix" although it was one of several tabs I opened up for perusal. The kicker was the first chapter having the mention of gardening and muscles, the second chapter having the gift from Ginny, and then poking around the final chapters to find where Dumbledore awards them "The Order of the Phoenix".
