OP, you are getting some stick here.
I absolutely get what you're saying. I don't think it's unreasonable to expect an adult, mother or father, to exercise a modicum of patience and kindness when putting their child to bed, and crucially, to be able to override their own impulse to act out any frustration or impatience with a 4 year old.
Posters are piling in to upbraid you for making a rod for your own back by not training your DD to fall asleep independently. How about your husband training himself, like the adult he is, to do a bit of adulting and moderate his own behaviour?
Your husband would absolutely not snap like this at a colleague or his sibling's child, so why should you and DD have to put up with it? Being impatient and venting frustration in this way is a character flaw, not a conscious and considered parenting choice. I can't bear people making excuses for men adults who can't put their own preferences (because that's all it is) to one side for a moment, in order to achieve an overall objective with a positive outcome. He doesn't need coaching or 'mancouragement' (boak, wtf!?), he needs to decide to regulate himself effectively.
I wonder if this situation where you step in has arisen because you know he's got potential for really snapping, and you worry he'll lose his rag? It's exhausting always being on the lookout for signs of a fraying patience or smouldering temper in an adult partner, and trying to shield others from it. His unwillingness to parent with patience and calmness will erode both yours and your DD's respect for and trust in him. Young kids see things very clearly and we absolutely do not do them any favours by making out that the kind of behaviour we teach them is undesirable (being trucculent, snappy, dismissive and impatient) is OK when an adult does it. Massively undermining of the child's developing emotional compass.
If I were you, I'd trade 100% of bedtimes with your husband in exchange for some other thing he can do, either nightly or weekly, but requiring a similar amount of time. Then I'd gradually do what a PP suggested and begin, slowly, to work on a gentle "I'm just popping to the loo, back in 5 minutes" transition. If your DD is relaxed and feels safe, this will be much more likely to succeed. But I'd also think very carefully about how much your DP's immaturity and unwillingness to switch up is impacting on your relationship and whether you are prepared to hang in there.
And some DC just take longer to get to the point of sleeping independently. Whenever I hear a parent say they're still sitting with their school aged child until they go to sleep every night, I don't judge or dismiss them; they go up in my estimation and I see that, whatever the reason, it must be tough, boring, worrying or frustrating, but they still show up. It doesn't last forever.