I had done more research on Musgrove to figure out what else could be driving the sizable differences between his ERA and FIP (as Fangraphs calls it E-F). As I noted the bad D of the Pirates and inconsistent BP play has a lot to do with it, but one thing I have overlooked is his pitching with men on base. This is what's keep his LOB% down, in other words more men scored against him when they get on base (again, some of this could be attributed back to the Pirates BP, but a lot of it is on him also). For his career, his overall OPS against is .740. However with men on base, it is .790, which is a pretty big difference compared to other pitchers. I sampled some of the pitchers with elite LOB%, and for their career, their overall OPS and OPS with men on base are about the same (granted some of these guys have the added luxury of pitching in front of elite BPs, e.g. Clevinger, Kershaw, Ryu), in fact, a guy like Verlander actually shifts to another gear with men on base the last 5 years, he's absolutely lights out. Even for a mid rotation starter, their difference is anywhere from marginal to .30 ish.
Now I haven't seen Musgrove pitch more than a start or two myself, I don't know how well he could pitch from the stretch, but that really seems to be inflating his ERA compared to his FIP the last few years. 2020 is actually a year he posted a strong LOB% (14% increase from 2019). However since 2020 stats are SSS, there isn't a large enough sample of ABs with men on base to truly tell if Musgrove has made real improvements pitching from the stretch, at least not without seeing him pitch.
I still believe he's an improved pitcher from 2019 based on his much improved secondary pitches, but I would say his ability to pitch from the stretch will be the determining factor between him being a legitimate #3 or even #2, or just a #4 starter with a shiny FIP and fWAR.