In a medium bowl, whisk the chicken broth, soy sauce, and fish sauce until combined; set aside.
Heat the vegetable oil in a wok or large skillet over medium-high heat until shimmering. Add the shrimp in a single layer and stir-fry until just pink, 1β2 minutes; transfer to a plate.
Add the chicken thighs to the wok and stir-fry until lightly browned and cooked through, 4β6 minutes; transfer to the plate with the shrimp.
Add the yellow onion and garlic to the wok and stir-fry until aromatic, 1β2 minutes.
Add the celery and carrot and cook until slightly tender, 2β3 minutes.
Pour in about half of the broth mixture and bring to a simmer, scraping up browned bits.
Add the bihon rice stick noodles and toss, adding the remaining broth mixture as needed, until the noodles soften and absorb most of the liquid, 4β6 minutes; the strands should be tender with a slight bite and no hard core.
Return the reserved plate contents and toss to combine evenly, 30β60 seconds.
Add the green cabbage and snow peas and cook until crisp-tender, 1β2 minutes.
Season with the ground black pepper and toss once more.
Transfer to a platter, top with the scallions, and serve with the calamansi.