Yes, but nowhere has she been complimented for it.
Im not sure she needs to be though lol. My whole argument for Carrot is that her role would almost feel "useless" in a way. Anyone could be a lookout, but its the fact that she does it all the time and gravitates to it is the point.
I personally think Luffy wont invite her, but she'll stowaway on the ship, just like she did before WCI. She WANTS to go on adventures. She WANTS to feel needed as indicated by that collage.
Yes I think Carrot will force herself on Luffy's ship post Wano and make the lookout position her own, regardless of how important she feels or how important she comes off. Oda drew those panels in that collage, and theres another set of panels that depict this. This is Oda showing it, not me.