The washing/cleaning/sweeping activities are signs of renewal. Really, I could end this post here; that pretty much says it.
If I did, though, I’d miss pointing out the sheer drollery of the conversation on p. 62:
“What are you doing?” cried Michael and Calcifer in a horrified chorus.
“Cleaning up,” Sophie replied firmly. “The place is a disgrace.”
Calcifer said, “It doesn’t need it,” and Michael muttered, “Howl will kick you out!” but Sophie ignored them both. Dust flew in clouds.
“It doesn’t need it…!?” How can Calcifer SAY such a thing, particularly when he’s already agreed to go along with the cleaning lady ruse? Is it because he’s a non-corporeal being and thus is neither aware of nor attuned to material clutter? Or is it just guy-speak? Howl himself seems unconcerned about the mess, so Calcifer is as well.
Michael, on the other hand, is broadcasting his own still-uncertain status in the household. He’s never pinned Howl down about anything, let alone whether he is welcome to go on staying there, and getting kicked out is probably always at the back of his mind. Plus I detect a bit of jealousy towards Sophie on the next page, when the doorknob goes blue-down and there’s a little girl from Porthaven there to pick up a spell for her dad’s boat.
“Has the Sorcerer got a witch working for him too?” she asked.
“No,” said Michael.
“Meaning me?” Sophie called. “Oh, yes, my child. I’m the best and cleanest witch in Ingary.”
Michael shut the door, looking exasperated. [Michael knows how rumors get started and spread.] “That will be all round Porthaven now. Howl may not like that.” 
Sophie cackles in reply. She doesn’t care. She’s cast off the grey mouse, she’s out of the hat shop, and she’s having the time of her life. She’s also just made herself the best and cleanest witch in Ingary.
Just as she notices that the fourth paint blob on the revolving doorknob is black, then sets to work on the cobwebs festooning the beams, Howl emerges from the bathroom. “He looked marvelously spruce.”  Other than that his suit looks brighter, that’s all we get of Sophie’s response.
She’s hoping to impress him with her diligence. He’s hoping to impress her with his gorgeousness. It seems to be working. Feelings are happening. This is uncomfortable for both of them. Best to change the subject; this Howl does by directing the conversation to spiders.